M4maths Previous Puzzles

23 Sep 2015 Time and distance

The ratio between the rates of walking of A and B is 2:3 and therefore A takes 10 minute more than the time taken by B to reach the destination. If A had walked at double the speed, he would have covered the distance in

OPtion

1) 15 minute
2) 20 minute
3) 25 minute
4) 30 minute
5) 35 minute
6) 40 minute
7) 45 minute
8) 10 minute
9) 5 minute
10)None of these

Solution

Ratio of time taken = 1/2 : 1/3 = 3:2
Suppose B takes x min. Then A takes (x+10) min
Therefore x+10 / x = 3/2
2(x+10) = 3x
x = 20
Thus, A takes 30 min

So with double speed it will take 15 min

Option 1)

Correct Option: 1 Best Solution (72)

ABHINAV PUSHPAM   9 years AGO

Ratio of speed = 2:3
Ratio of time = 3:2
A takes 10 min more
3x-2x = 10 min
A time=30 min
A covers the distance in 30 min , if its speed is x
So, He will cover the same distance in 15 min, if its speed
doubles (i.e 2x)

option 1)

Like? Yes (26) | No (4)  

MADHUBABU   9 years AGO

ratio of times of A&B =1/2 : 1/3
If B takes x min, then A takes (x+10) min
therfore (x+10) :x=1/2 : 1/3
=> (x+10)/x =3/2
=> 2x+20= 3x
=> x= 20 min
therfore time taken by A =20+10=30 min
If A had walked at double speed
required time = 30/2 = 15 min.

Like? Yes (14) | No   

sudiptaa   9 years AGO

Ratio of times = 1/2 :1/3
when speed of A is doubled = 4
time taken by A = 1/4*60 = 15 mintutes

Like? Yes (11) | No   

praveendas   9 years AGO

ratio of time taken by them is 3:2 for a certain distance.
given time diff is 10 so times are30:20,
if a doubled his speed then time taken is reduced to half which is 15 min.
option 1

Like? Yes (5) | No   

chinu singla   9 years AGO

As we know speed=1/time;
let time taken by B= x
thus,time taken by A= x+10;
therefore x+10/x=3/2
after solving it we get x=20
thus time taken by A= 20+10=30
AND IF A doubles its speed then its time gets halved
so time taken by A after doubling its speed=30/2=15

Like? Yes (5) | No   

Aman   9 years AGO

A/B=2/3
i.e
A=2
B=3
so
according to equation of speed = distance / time
we got that
let x be the time taken by B
so X+ 10 is the time taken by A
so
2=distance/x+10
and
3= distance / x
now
equating distances
2(x+10)=3x
so
x=20
so
time taken by A= 30
now speed is inversly proportional to time so
if speed doubles time reduces by half
so
time taken by A= 15 Minutes

Like? Yes (5) | No   

ramakrishnateja   9 years AGO

given the rates ratio is 2:3 which means sa:sb=2:3 ta=tb+10. here d is same so 2t1=3t2. 2(t2+10)=3t2 t2=20. hence t1=30.if sa becomes 2sa then t=d/2sa . here d=2t1=2*30=60. sa=2 hence t=60/4=15min.

Like? Yes (4) | No   

avanthika   9 years AGO

Time will be halved 30/2=15min

Like? Yes (6) | No (2)  

SAGNIK DATTA   9 years AGO

(d/2x) - (d/3x) =10 so d= 60x now d/4x = 15 min

Like? Yes (4) | No (1)  

kriti kankariya   9 years AGO

let the speeds be 2x and 3x of A & B rsp
then,
d/2x = d/3x +10 (given A takes 10 min more than B)
solving,d=60x
then if A's speed will be doubled then time taken will be
d/4x
= 60x / 4x
=15 min

Like? Yes (3) | No   

vinusha   9 years AGO

Speed is inversely proportional to time
So when speed doubles, time will be halved
30/2=15min

Like? Yes (3) | No   

Nikhil chavan   9 years AGO

x/y=2/3...3x=2y...D/x=10+D/y...gives D=30x..so we require D/(2x)=15

Like? Yes (3) | No (1)  

Moutam Vishnu Murthy   9 years AGO

Ratio of speed=2:3
Ratio of time=3:2
let A takes 3x hrs,B takes 2x hrs
then 3x-2x=10/60 hr
x=1/6 hr
Time taken by A to reach the destination is 3x= 3*1/6= 30mins
If A had walked at double the speed he will reach in 15mins.

Like? Yes (2) | No   

Testing Account   9 years AGO

4

Like? Yes (2) | No   

rahul shaw   9 years AGO

diff between their ratio is 1=10 min
2:3=is the walking speed ratio
time ratio is 30:20
since their diff is 10
so
.if A doubles its speed then he would reach in 15mins

Like? Yes (2) | No   

TONI PRIYA   9 years AGO

let B takes time t,then A will take (t+10) time
so (x/(t+10))/(x/(t))=2/3
after solving this we will get t=20.
t+10=30.
That's why A takes 30 min
In that way,if A had walked at double speed,he would have covered the distance in 15 min.

Like? Yes (1) | No   

sravani   9 years AGO

speed is inversely proportional to time so,
time will be x/2 and x/3
x/2-x/3=10min
x=60 mins
so,A takes 30 mins at present
If speed is doubled then time will be 15 mins.

Like? Yes (1) | No   

RENU KUMARI   9 years AGO

s1=2*(2/3s2)
d/t1=2*(2d/3t2)
t1=t2+10
so, t2=5
and t1=15

Like? Yes (1) | No   

Divyashree   9 years AGO

ratios of speeds of A and B is 2:3
ratios of time taken by A and B is 3:2
A/B=3/2
2A=3B
given A=B+10
A=(2A/3)+10
A=30
B=20
if A has walked at double the speed,he would have covered the distance in 15 minutes
therefore, ans is 1)15 minutes

Like? Yes (1) | No   

S.Hemanth kumar   9 years AGO

the ratio of a @b is =1/2:1/3
suppose B takes x min then A takes x+10 min
so x+10/x =3/2
x=20
A=20+10=30
A takes double speed so
t=30/2=15 minutes

Like? Yes (1) | No   

shiuli noor alam   9 years AGO

A will cover the same distance with double speed in 15 minutes.

Like? Yes (1) | No   

Tanya Sachdev   9 years AGO

A with previous speed covers the distance in 30 min if the speed is doubled time reduced to half 15 min

Like? Yes (1) | No   

Surendra Naraga   9 years AGO

Ratio of speed = 2:3
Ratio of time = 3:2
A takes 10 min more
3x-2x = 10 min
A time=30 min
A covers the distance in 30 min , if its speed is x
-> He will cover the same distance in 15 min, if its speed
doubles (i.e 2x)

Like? Yes (1) | No   

Shubham Raj   9 years AGO

right answer is 15 min
option-1

Like? Yes (1) | No   

Gugulothu vijaykumar   9 years AGO

Ratio of speed = 2:3
Ratio of time = 3:2
A takes 10 min more
3x-2x = 10 min
A time=30 min
A covers the distance in 30 min , if its speed is x
-> He will cover the same distance in 15 min, if its speed
doubles (i.e 2x)

Like? Yes (1) | No   

H. Sreekanth   9 years AGO

Ratio of speed = 2:3
Ratio of time = 3:2
A takes 10 min more
3x-2x = 10 min
A time=30 min;
A covers the distance in 30 min , if its speed is x
- He will cover the same distance in 15 min, if its speed
doubles (i.e 2x)

Like? Yes (1) | No   

venkatesh   9 years AGO

a:b=2:3
a=b+10
b=20
a=30
but double the speed
so a=30/2=15
s0 15

Like? Yes (2) | No (1)  

pravallika   9 years AGO

case i:speed is inversely proportional to time
so,2/3=t/(t+10)
implies 3t=2t+20;t=20;
it means a covers it in 30 min.
case ii)if speed of a doubles ,then 4/3=20/t
implies t=15 min.
therefore,if speed of A doubles,then he covers the distance in 15 min.

Like? Yes (1) | No   

aditi kumari   9 years AGO

let a speed is 2 m/sec and B speed is 3 m/sec and time taken by A to reach destination is X sec.
THEn according to question time taken by B =X-10 sec.
2X=3(x-10)
x=30 sec.
total distance cover =30* 2=60m.
now if A double his speed then speed =4m/sec.and now time taken by a =60/4=15 sec.

Like? Yes (1) | No   

Pesari Udayasree   9 years AGO

ratio of speed and time as 2:3 and 3:2
let a takes 3x hrs and b takes 2x hrs then 3x-2x=10/60hr
x=1/6 hr
then 3x=3(1/6)=30 min.which is the time taken by a to reach the destination
if a had walked at double the speed he will reach in 15min.
so answer is 15min.

Like? Yes (1) | No   

SUMIT PAREEK   9 years AGO

Ratio of times taken by A & B=1/2 : 1/3
let B takes x min , then A takes (x+10) min
(x+10 : x)=1/2 : 1/3
so, (x+10)/x=3:2
x=20
time taken by A=20+10=30 min
If A had walked double speed , then
required time = 30/2= 15 min

Like? Yes (1) | No   

Abhijit Das   9 years AGO

Ta =Tb + 10
D/2x = D/3x + 10

therefore , D= 60x
speed doubled 2* 2x= 4x
60x/4x = 15
ans= 15 mins

Like? Yes (1) | No   

NITESH KUMAR SINGH   9 years AGO

let thec speed be 100
so speed of a=40 and speed of b=60
time taken by a=x/40
and b=x/60
so x=1200
and speed=80
sotime=1200/80=15min

Like? Yes (1) | No   

Anup Sahay   9 years AGO

let speed and time of A be s1 and t1 and let speed and time of B be s2 and t2
so speed to time ratio : s1/s2=t2/t1
so, 2/3=t2/t2+10
t2=20 mins
so t1=30 mins
now d=s1*t1=2*30=60
so if
60=4*s1'
s1'=15 mins answer

Like? Yes (1) | No   

chetan   9 years AGO

actual time=30 mins
if doubles the speed 15 mins

Like? Yes (1) | No   

ramya   9 years AGO

Speed = Distance / time.
Based on the ratios the option is 1)

Like? Yes (1) | No   

Arvind kumar   9 years AGO

If ratio is 2:3 and A takes 10 minute more than A takes 30 minute and B takes 20 minute.
therefore,if A walked with double speed , he would cover the distance in 15 minute.

Like? Yes (2) | No (1)  

GURRAM MAHENDRA   9 years AGO

Ratio of speed = 2:3
Ratio of time = 3:2
A takes 10 min more 3x-2x = 10 min
A time=30 min
-->A covers the distance in 30 min , if its speed is x
-> He will cover the same distance in 15 min, if its speed
doubles (i.e 2x)

Like? Yes (1) | No   

vaibhavi lodhiya   9 years AGO

23=x/x+10;so t=60/4
T=15min

Like? Yes (1) | No   

gaurav singh   9 years AGO

Ratio of speed = 2:3
Ratio of time = 3:2
A takes 10 min more
3x -2x = 10 min
A time=30 min
A covers the distance in 30 min , if its speed is x
He will cover the same distance in 15 min, if its speed
doubles

Like? Yes (1) | No   

Rohit Agrawal   9 years AGO

d/2x=d/3x+10
=>d/x=60
=>d/4x=15 ... answer

Like? Yes (1) | No   

patki shrikant   9 years AGO

speed double time half.
so now time taken by a =30
again speed double time half=15

Like? Yes (1) | No   

Deepanshu Chaturvedi   9 years AGO

let y be time taken.from question x/30=y and x/20=y+1/6 solving we get y=1/3 hours=20 minutes.'A' takes 10 minute more means 30 minutes.doubling speed means time become half i.e.15 minutes.

Like? Yes (1) | No   

sandeep prasad   9 years AGO

the ratio is 20 min and 30 min so if a take 30 min by x speed then he take 15 min by 2x speed

Like? Yes (2) | No (1)  

kandi sindhuja reddy   9 years AGO

Speeds a:b is 2:3,let time taken by b is x,then speed is inversely propirtional to time,i.e., 2:3=x:x+10,x=20,then time taken by a is 30mins,if speed of a is doubled then time will be half then a takes 15mins.

Like? Yes (1) | No   

Sayandeep Jana   9 years AGO

A takes=x+10 min
B takes=x min
using ratio we get x=30

Like? Yes (1) | No   

nirmal das   9 years AGO

let speed of A and B is 2x and 3x and distance is y...
so (y/2x)-(y/3x0=10 fromthis we get y=60x
now 60x/4x=15 so A takes 15 minutes

Like? Yes (1) | No   

Ashish Kumar Singh   9 years AGO

let's assume that B take x min to cover then A takes x+10 min to cover same distance.
3x=(x+10)2
x=20 min
A takes 30 min.
If speed of A is double.
then he takes 15 min.

Like? Yes (1) | No   

Belal Ahmed   9 years AGO

let the distance be x
then x/2 - x/3 = 10
x=60
if a's speed is double the time is 60/4=15mins

Like? Yes (1) | No   

utkarsh mittal   9 years AGO

let distance be x and A speed be 2y and B speed be 3y
x/2y-x/3y=10
x = 60y
then time of A is 15 min

Like? Yes (1) | No   

YASWANTH REDDY   9 years AGO

let speeds of A and B be 2V and 3V respectively.
As time and velocity are inversely proportional, and t be the time taken by B to reach the destination, then
2/3 = t/(t+1/6) and we get t = B's time = 20 min, and A's time = 30 min. If he travels with double speed, then time gets halved and therefore time taken by A to reach the destination with double the speed = 15 min

Like? Yes (1) | No   

Divya   9 years AGO

First take A:B=2:3 that means speeds in ratio of 2:3 and given time by A is t+10 and B is t and then by solving with equal distance then we get t=20.After that as speed is doubled we get 15 minutes as answer

Like? Yes (1) | No   

Siva   9 years AGO

Let the speeds of A and B are 2x and 3x respectively. The time taken by B be t, then the time taken by A is t+10.
2x(t+10)=3xt,
2xt+20x=3xt,
xt=20x,
t=20.
The time taken by B is 20, so time taken by A is 30.
(S1:S2)=(T2:T1),
(S1:2 S1)=(T2:30),
T2=(30÷2)=15.
If the A walk at double speed he will reach in 15 minutes.

Like? Yes (1) | No   

Subhasri Pal   9 years AGO

Let the speeds of A and B be 2x and 3x respectively.
and time taken by A and B be y+10 and y respectively.
therefore equating,
2x(y+10)=3xy
or,2xy+20x=3xy
or,xy=20x
0r,y=20
so, y+10=30.
so time taken by A is 30 mins.
therefore, if the speed of A is doubled time taken would be halved.
hence, 15 mins.

Like? Yes (1) | No   

akanksha    9 years AGO

Time taken by A is =time taken by B-10
Distance/2x=distance/3x-10
Distance=60x
If speed of A double then time =
60x/2×2x
=15 min

Like? Yes (1) | No   

PAWAN KUMAR   9 years AGO

1/4 *60 MIN = 15 MIN.

Like? Yes (1) | No   

Sinthiya Jana   9 years AGO

let distance=n,
speed of A and B is 2x and 3x respectively.
then,
n/2x-n/3x=10
=>n/x=60
now time taken by A is n/2x=60/2=30
and time taken by B is n/3x=60/3=20
total time=50
now speed of A become 4x.
so time taken by A is 60/4=15

Like? Yes (1) | No   

pradyumn   9 years AGO

let x is distance
so x/2 = x/3+10
-> x= 60
now new speed = 4
-> time = 15

Like? Yes (1) | No   

sireesha.yammanuru   9 years AGO

Given ratio of the speeds of A,B is
A : B = 2X:3X---(1)
let At = time taken to reach destination by A & smiliarly Bt by B
given At = Bt+10 min --(2)
we know that speed�time = constant for same distance
A�At = B�Bt --(3)
solving above 3 equations we get
At = 30 min
for a speed of 2X it takes 30 min
then for a double speed i.e 4X speed it takes 15 min only.. bcse s�t = dstane (constant)

Like? Yes (1) | No   

Kiran Notwani    9 years AGO

Rate is 2/3
Suppose B takes X minutes so A takes X+10 minutes

Hence 2/3=X/X+10

X gives 20 hence B Takes 20 minutes and A takes 30

At double speend A will take only 15

Like? Yes (1) | No   

diksha   9 years AGO

speed is inversly propotional to time.
so if speed is doubled, time will be half .
At first speed of A, time can be calculated by equalling the distance travelled by both A & B

Like? Yes (1) | No   

jayaram   9 years AGO

Ratio of times taken by A and B=1/2:1/3
suppose Btakes x min.Tehn A takes (x+10)min
(x+10):x=1/2:1/3
(x+10)/x=3/2
2x+20=3x
x=20;
Time taken by A=20+10=30;
if A walked at double speed
=30/2=15min

Like? Yes (1) | No   

ANKUR BAJWA   9 years AGO

Speed of A=2x
Speed of B=3x
time taken by B=t mins
time taken by A=(10+t) mins
from formula s=v*t
distance covered by A=Distance covered by B
2x * (10+t)=3x * t
20 + 2t=3t
t=20 mins
So time taken by A=20+10=30 mins
And Time taken by B=10 mins
Now speed of A is double so speed of A=2*2x=4x
But distance is same
So time taken by A to covered this distance by double speed=t1
So
again from s=v*t
distance covered by A with 2x speed=distance covered by B with 4x speed
2x * 30=4x*t1
60=4t1
t1=15 mins (answer)

Like? Yes (1) | No   

swathi   9 years AGO

Ratio of speed = 2:3
Ratio of time = 3:2
A takes 10 min more
3x-2x = 10 min
A time=30 min
ÆA covers the distance in 30 min , if its speed is x
-> He will cover the same distance in 15 min, if its speed

Like? Yes (1) | No   

dhriti gupta   9 years AGO

d/2x=d/3x+10 solving and equating using this equation

Like? Yes (1) | No   

Arijit Bera   9 years AGO

S(A)-2a*(b+10) ,S(B)-3ab [b=time]
time taken by A=2a(b+10)/4a
solving previous eqation get b=20
so A(t)-15

Like? Yes (1) | No   

pravin singh   9 years AGO

Ratio of speed = 2:3
Ratio of time = 3:2
A takes 10 min more
3x-2x = 10 min
A time=30 min
A covers the distance in 30 min , if its speed is x
He will cover the same distance in 15 min, if its speed
doubles (i.e 2x)

Like? Yes (1) | No   

Aritra Chakraborty   9 years AGO

A speed = 2k
B speed = 3k
total time taken by B to cover the distance = t
i.e., total distance = 3kt
time taken by A = t+10
i.e., total distance = 2k(t+10)

3kt = 2k(t+10) => t = 20
thus total distance = 60k

double A speed = 4k
time req = 60k/4k = 15 min

Like? Yes (1) | No   

premlata   9 years AGO

ratio of time is reciprocal to speed.

Like? Yes (1) | No   

kiran   9 years AGO

1/2:1/3=x:10
x=15min

Like? Yes (1) | No   

Amit chaturvedi   9 years AGO

Ratio of speed = 2:3
Ratio of time = 3:2
A takes 10 min more
3x-2x = 10 min
A’s time=30 min
A covers the distance in 30 min ,if its speed is x
He will cover the same distance in 15 min,
if its speed doubles (i.e 2x)

Like? Yes (2) | No (1)  

siddhi datri   9 years AGO

Let the time taken by A be t.
then, B will take t-10
therefore,2/3=t-10/t
=>t=30 mins
now if speed is doubled den time will be halved because distance is same
Then New time will be 30/2=15 mins.

Like? Yes (1) | No   

22 Sep 2015 Possibility

A correspondent writes 7 letters and addresses 7 envelopes, one for each letter. In how many ways can all of the letters be placed in the wrong envelopes?

OPtion

1) 1576
2) 1876
3) 1954
4) 1896
5) 1856
6) 1754
7) 1854
8) 1756
9) 1676
10)1858

Solution

1854
According to this mathematical formula: 7! (1/2 ! - 1/3 ! + 1/4 ! - 1/5 ! + 1/6 ! - 1/7) = 1854

Option 7)

Correct Option: 7 Best Solution (30)

RAKESH   9 years AGO

7! * ( 1/2! - 1/3! + 1/4! - 1/5! + 1/6! - 1/7! )

= 2520 - 840 + 210 - 42 + 7 - 1

= 1854

Like? Yes (8) | No (3)  

payal   9 years AGO

ans is 18 54
no letter in right envelope=
n![1-1/1!+1/2!-1/3!+.......1/n!]
here n= 7

Like? Yes (5) | No   

Sanjeev Kumar   9 years AGO

by using the formula D(n)=n! * (1/2! - 1/3! +1/4! - .... +(-1)^n/(n!) )

Hence D(7)=1854

Like? Yes (3) | No (1)  

SOURABH   9 years AGO

1854
formula is n!(i/2!-1/3!+......+(-1)^n/n!)

Like? Yes (3) | No (1)  

patki shrikant   9 years AGO

n!(1/2!-1/3!+1/4!........(-1)^n*1/n!

here n=7

Like? Yes (3) | No (1)  

alpesh kurhade   9 years AGO

Number of ways in which 'n' objects can be placed on 'n' positions in such a manner that none of them is correct is given by the Dearrangement formula.

D(n)= n!(1/2!-1/3!+1/4!........(-1)^n*1/n!).

Dearr(7) = 7! * (1 - 1 + 1/2 - 1/6 + 1/24 - 1/120+1/6!-1/7!)

ans- 1854

Like? Yes (3) | No (1)  

Abhinav Akash   9 years AGO

According to this mathematical formula: 7! (1/2 ! - 1/3 ! + 1/4 ! - 1/5 ! + 1/6 ! - 1/7) = 1854

Like? Yes (4) | No (3)  

sudiptaa   9 years AGO

6 cases for the first, 5 for the second, 4 .. Wait a bit--suppose the first and second just swapped? Start from the beginning.

1 letter, always right, =0
2 letters, one way to goober it up
3 letters, 2 ways
4 letters: ah. 3*2=6 ways of cycling the 4 around, but then 3 ways of doing 2+2. (=9)

So partitioning is the way to go. A partition of 1 always maps the letter into the right envelope, so there's no answers with partition 1.

7 can be
a "cycle" of 7: with 1 case, which has 6*5*4*3*2 permutations
a "cycle" of 5 plus a "cycle" of 2: with 7*6/2 cases and 4*3*2 permutations
a "cycle" of 4 plus a "cycle" of 3: where I'm going to cheat and include the 2+2 in the 4, with 7*6*5/6 cases and (2 {for the 3} * 9 {for the 4}) permutations

That gives me 720+504+630=1854

Like? Yes (1) | No   

TONI PRIYA   9 years AGO

for dearrangement Dn=n!(1/2!−1/3!+1/4!−....)
here n=7
Dn=7!(1/2!-1/3!+1/4!-1/5!+1/6!-1/7!)
=1852.2...
so nearest is 1854

Like? Yes (1) | No   

DIPAK TIWARI   9 years AGO

According to the mathematical formula: 7!(1/2! -1/3! + 1/4!- 1/5! +1/6! -1/7!)=1854
option 7

Like? Yes (1) | No   

sukriti singh   9 years AGO

from formula of dearrangement we get
n![1-1/1!+1/2!-1/3!+1/4!-1/5!+1/6!-1/7!]
n=7
we get ans as 1854..

Like? Yes (2) | No (1)  

akhil   9 years AGO

if there are n things in a row, a permutation of these n things such that none of them occupies its original position. then total no of ways =
n!((1/2!)-(1/3!)+(1/4!)-(1/5!)+......+(-1)^n(1/n!))

Like? Yes (2) | No (1)  

Raj jariwala   9 years AGO

D(N)=(N-1)[D(N-1)+D(N-2)]

AND D(2)=1,D(1)=0
ANS IS 1854

Like? Yes (2) | No (1)  

ramakrishnateja   9 years AGO

probability of placing atleast 1 letter into correct envelope + probability of placing none into correct envelope =1
so prob of placing atleast 1 into correct envelope is 1-1/2!+1/3!-1/4!+1/5!-1/6!+1/7! hence the other prob is 1-above result. i.e, 1/2!-1/3!+1/4!-1/5!+1/6!-1/7! =1854/5040.hence the num of ways =1854 out of 5040 ways.

Like? Yes (1) | No   

kannya   9 years AGO

7!*[ 1/2! - 1/3! + 1/4! - 1/5! + 1/6! - 1/7! ]
ans is 1854

Like? Yes (1) | No   

chinu singla   9 years AGO

7!(1-1/1!+1/2!-1/3!+1/4!-1/5!+1/6!-1/7!)
=1854

Like? Yes (1) | No   

K.H.Ravali   9 years AGO

no. of de arrangements =n!{(1/2!)-(1/3!)...........(-1)^n/n!}

Like? Yes (1) | No   

Satya Samhitha Papineni   9 years AGO

The number of derangements is: n!(1/2!-1/3!+.....+(-1)^n/n!)

Like? Yes (1) | No   

vikash kumar das   9 years AGO

as the formula is given by no of ways=n!(1-1/1!+1/2!-1/3!+....+1/n!)

on putting n=7 we get 1854.

Like? Yes (1) | No   

Aman   9 years AGO

according to formula
7!(1/2!-1/3!+1/4!-1/5!+1/6!-1/7!)
so on solving it deeply 1854 is the answer

Like? Yes (1) | No   

MADHUBABU   9 years AGO

7!{(1/2!)-(1/3!)+(1/4!)-(1/5!)+(1/6!)-(1/7!)}

Like? Yes (2) | No (2)  

komal sharma   9 years AGO

to find the answer formula is n!(1-1/1!+1/2!-1/3!+.....(-1)1/n!)
so here n is 7
after solving this we get 1854
.

Like? Yes (2) | No (2)  

SUMIT PAREEK   9 years AGO

1854
According to this mathematical formula: 7! (1/2 ! - 1/3 ! + 1/4 ! - 1/5 ! + 1/6 ! - 1/7) = 1854

Like? Yes (2) | No (2)  

SHAIK MAHABOOB BASHA   9 years AGO

according to this mathematical formula:7!(1/2!-1/3!+1/4!-1/5!+1/6!-1/7!)=1854

Like? Yes (1) | No (1)  

GURRAM MAHENDRA   9 years AGO

according to permutataions and combinations
the output=7![(1/2)!-(1/3)!+(1/4)!-(1/5)!+(1/6)!-(1/7)!]=1854

Like? Yes (1) | No (1)  

H. Sreekanth   9 years AGO

According to this formula=7!*(1/2!-1/3!+1/4!-1/5!+1/6!-1/7!)

Like? Yes (1) | No (1)  

ABHINAV PUSHPAM   9 years AGO

1 letter, always right, =0
2 letters, 1 way
3 letters, 2 ways
4 letters: ah. 3*2=6 ways of cycling the 4 around, but then 3 ways of doing 2+2. (=9)

So partitioning is the way to go. A partition of 1 always maps the letter into the right envelope, so there's no answers with partition 1.

7 can be
a "cycle" of 7: with 1 case, which has 6*5*4*3*2 permutations
a "cycle" of 5 plus a "cycle" of 2: with 7*6/2 cases and 4*3*2 permutations
a "cycle" of 4 plus a "cycle" of 3: where I'm going to cheat and include the 2+2 in the 4, with 7*6*5/6 cases and (2 {for the 3} * 9 {for the 4}) permutations

That gives Answer as 720+504+630=1854

Option 7)

Like? Yes (5) | No (6)  

shivam dubey   9 years AGO

6 cases for the first, 5 for the second, 4 .. Wait a bit--suppose the first and second just swapped? Start from the beginning.

1 letter, always right, =0
2 letters, one way to goober it up
3 letters, 2 ways
4 letters: ah. 3*2=6 ways of cycling the 4 around, but then 3 ways of doing 2+2. (=9)

So partitioning is the way to go. A partition of 1 always maps the letter into the right envelope, so there's no answers with partition 1.

7 can be
a "cycle" of 7: with 1 case, which has 6*5*4*3*2 permutations
a "cycle" of 5 plus a "cycle" of 2: with 7*6/2 cases and 4*3*2 permutations
a "cycle" of 4 plus a "cycle" of 3: where I'm going to cheat and include the 2+2 in the 4, with 7*6*5/6 cases and (2 {for the 3} * 9 {for the 4}) permutations

That gives me 720+504+630=1854

Like? Yes (1) | No (2)  

praveendas   9 years AGO

let take 2 envelopes .for above condition ,possibility is 1
for 3 possibility is 2
for 4 it is 8
.
.
.
.
.

for 7 it wil be1854

Like? Yes (2) | No (4)  

Ajay Kumar Gupta   9 years AGO

a/c to mathematical formula=7!(1/2!-1/3!+1/4!-1/5!+1/6!-1/7!)
=1854

Like? Yes (1) | No (3)  

21 Sep 2015 Arrangement

If 6 3 5 4 2 equals 5 2 6 3 4, what is B C D E F?

OPtion

1) C F B D E
2) E F B C D
3) D F E C B
4) D C B F E
5) E F B C D
6) D F C E B
7) D B F C E
8) D F B C E
9) F D B C E
10) None of these

Solution

D F B C E
The letters must be transposed in the same order as the numbers.

Option 8)

Correct Option: 8 Best Solution (66)

praveendas   9 years AGO

6=B,3=C,5=D,4=E,2=F,,,
For 52634 it is DFBCE.that's it..
option 8

Like? Yes (6) | No   

Amit chaturvedi   9 years AGO

63542 equals 52634

B=6,C=3,D=5,E=4,F=2 so now
52634 i.e DFBCE

Like? Yes (2) | No   

priyanka burnwal   9 years AGO

bcdef=23456
if 63542=52634
then23456=46235
so
46235=dfbce

Like? Yes (2) | No   

ramya   9 years AGO

The letters are just rearranged based on above

Like? Yes (1) | No   

MRITUNJAY   9 years AGO

arrange according to above series

6 3 5 4 2

5 2 6 3 4
similarly
d f b c e

Like? Yes (1) | No   

Sruthi Sreejan   9 years AGO

6 3 5 4 2
5 2 6 3 4

Here the positions are rearranged where first becomes the third 2nd becomes 4th 5 th becomes 2nd etc.
hence
B C D E F =
D F BC E

Like? Yes (1) | No   

Shubham Raj   9 years AGO

from ques-
6 3 5 4 2 (arrange as) --> 5 2 6 3 4
B C D E F (arrange as) -->D F B C E (we put letter place of 5,2,6,3,4)

Like? Yes (1) | No   

TAUSEEF AMEEN   9 years AGO

given:
63542=52634...
in this eqn first digit is equal to third
second digit is equal tofouth
third digit is equal tofirst
fourth digit is equal to fifth
fifth digit is equal to second.
hence...similarly placing given sequence BCDEF
we got sequence as DFBCE..
Hence option 8 is correct.

Like? Yes (1) | No   

sudiptaa   9 years AGO

interchanging positions of 6 3 5 4 2 == 5 2 6 3 4
so , B C D E F === D F B C E

Like? Yes (1) | No   

Meenakshi   9 years AGO

6 3 5 4 2 => 5 2 6 3 4
Sorting Order is
3 5 1 2 4
Similarly
B C D E F => D F B C E
option 8)

Like? Yes (1) | No   

Arvind kumar   9 years AGO

middle one comes to first pos and last one comes to 2nd pos and first one comes to middle pos

Like? Yes (1) | No   

Arnab Maity   9 years AGO

just by observation I got this .. see the numbers and respectively place the alphabets

Like? Yes (1) | No   

TONI PRIYA   9 years AGO

6 3 5 4 2
6
3
5
4


||lly b c d e f
b
c
d
e
f

Like? Yes (1) | No   

YASWANTH REDDY   9 years AGO

the same pattern of rearranging the numbers has to be followed to rearrange the alphabets and we get the result.

Like? Yes (1) | No   

akanksha    9 years AGO

63542 equals 52634
Position of 6 changes to 3rd
Similarly position will change of all the number
By changing same postion of bcdef we will get dfbce

Like? Yes (1) | No   

Paul Rohit   9 years AGO

numbers in 6 3 5 4 2 are interchanged to 5 2 6 3 4, so B C D E F are interchanged to D F B C E

Like? Yes (1) | No   

Sonu kumar   9 years AGO

6 3 5 4 2 similar B C D E F

5 2 6 3 4 D F B C E
JUST CHANGE THE POSITION ..NOTHING ELSE. ..

Like? Yes (1) | No   

CHANDAN KUMAR   9 years AGO

let
C1 C2
row1 (6)f = e (5)
row2 (3)c = b(2)
row3 (5)e = f(6)
row4 (4)d = c(3)
row5 (2)b = d(4)

Here ,
row1 =row3 c2 Value
row2 =row4 c2 value
row3 =row1 c2 value
row4 =row5 c2 value
row5 =row2 c2 value

in the same way for

row1 (2) b = (4) d
row2 (3) c =(6) f
row3 (4) d= (2) b
row4 (5) e= (3) c
row5 (6) f = (5) e

ans will be DFBCE

Like? Yes (1) | No   

Deepak Kumar Sahu   9 years AGO

according to arrangement
1st digit go to 3rd place
2nd to 4th place
3rd to 1st place
4th to 5th place
5th to 2nd place

so BCDEF will be DFBCE

Like? Yes (1) | No   

ATTARU NASIMUNNI   9 years AGO

6 3 5 4 2 the arrangement changed like 5 2 6 3 4
likewise B C D E F is converted to D F B C E

Like? Yes (1) | No   

pepakayala laxmi tharaka manikanta   9 years AGO

by comparing the numbers and then arrange the alphabets as per the number places

Like? Yes (1) | No   

R.Shyaam Sunder   9 years AGO

arrange 6 3 5 4 2
B C D E F
5 2 6 3 4
ANS= D F B C E=>OPTION (8)

Like? Yes (1) | No   

Himanshu Rajpoot   9 years AGO

IF 6=B, 3=C, 5=D, 4=E, 2=F
according to that series
D F B C E

Like? Yes (1) | No   

Keval Tanna   9 years AGO

relate the given sequence with alphabets and rearrange them accordingly

Like? Yes (1) | No   

siddhi datri   9 years AGO

6 3 5 4 2
5 2 6 3 4
therefore
B C D E F
D F B C E

Like? Yes (1) | No   

GURRAM MAHENDRA   9 years AGO

in above the digit 6-->shifted to 3 poition
digit 3-->shifted to 4th postion
digit 5 hifted to first position
digit 4 shifted to 5th position
digit 2 shifted to second position
3 4 1 5 2
similarly B C D E F => D F B C E

Like? Yes (1) | No   

Pesari Udayasree   9 years AGO

ans:D F B C E
given 6 3 5 4 2 as
5 2 6 3 4 (just order changed)
in similar fasion by arringing B C D E F we get
D F B C E which is the required answer.

Like? Yes (1) | No   

praveen   9 years AGO

the places changes where 6 in first place goes to middle place in the second word..thus all the words jumbled..
So B should be in middle in the resulting word.
C should be in last but one place and so on.
So the result is DFBCE
OPTION 8

Like? Yes (1) | No   

Daniel Prabhakaran N   9 years AGO

63542 is the given order and we considered that as 12345.The order change to 35124 .likewise,BCDEF is considered as 12345 it should change into 35124 order.so,the answer is DFBCE.(option-8)

Like? Yes (1) | No   

umang agarwal   9 years AGO

we have arrange accordingly which is
1st pos=3rd pos;
2nd pos=4th pos;
3rd pos=1st pos;
4th pos=5th pos;
5th pos=2nd position.

Like? Yes (1) | No   

Mayur jaiswal   9 years AGO

its B-6,C-3,D-5,E-4,F-2
AFTER CONVERSION->D-5,F-2,B-6,C-3,E-4.

Like? Yes (1) | No   

kriti kankariya   9 years AGO

63542 is arranged as 52634
according to the places the gained BCDEF will be arranged as DFBCE

Like? Yes (1) | No   

Thaker Maulik   9 years AGO

63542 = 52634 accordingly take BCDEF instead of 63542
now, 63542=BCDEF so
52634= DFBCE so option 8 is correct

Like? Yes (1) | No   

Rakhi Modi   9 years AGO

Sequence of the number is given if we take alphabets as number then we get the answer

Like? Yes (1) | No   

Kethineni Vinodh   9 years AGO

6=B,3=C,5=D,4=E,2=F,,,
52634 it is D F B C E.that's it..

Like? Yes (1) | No   

Ashutosh Kumar Mantoo   9 years AGO

63542=51634 carefully check the position of the number we can easily find that
BCDEF=DFBCE

Like? Yes (1) | No   

PURNA   9 years AGO

As per the numbers rearranged in the given condition if alphabets are arranged it will produced a sequence DFBCE

Like? Yes (1) | No   

AMAN KUMAR SHAH   9 years AGO

lf we name the given 5 digit number by 1,2,3,4,5 and see this arrangement we see the format becomes 3,5,1,2,4.
same thing I did with the alphabetical arrangement.

Like? Yes (1) | No   

AMAN TURATE   9 years AGO

6 3 5 4 2 has changed to
1st- 3rd digit (5)
2nd- 5th didgit(2)
3rd - 1st digit(6)
4th- 2nd digit(3)
5th- 4th digit(4)
similarly we will do for B C D E F

Like? Yes (1) | No   

Darpan Pursnani   9 years AGO

comparing BCDEF with 63542, gives value for respective alphabets and then arranging alphabets according to 52634

Like? Yes (1) | No   

rahul shaw   9 years AGO

6=B, 3=C, 5=D, 4=E, 2=F
5 2 6 3 4=D F B C E
So option 8

Like? Yes (1) | No   

keerthi choudhry   9 years AGO

since the no in 10000th place is moved to 100thplace,1000th place no to 10thplace,100th place no to10000th place,10th place no to unit and unit place no to 1000th place
the answer for B C D E F is D F B C E

Like? Yes (1) | No   

jatin garg   9 years AGO

6 3 5 4 2 as 5 2 6 3 4
then if we judge the positions changed
then B C D E F will be D F B C E

Like? Yes (1) | No   

ramakrishnateja   9 years AGO

given that 63542 is equal to 52634 which means 1st letter is moved to 3rd & 3rd moved to 1st next 5th to 2nd and 4th to 5th and in 4th place remaining letter c is placed. likewise bcdef is changed to dfbce.

Like? Yes (1) | No   

Siva   9 years AGO

the order of the answer is as per the replacement of numbers

Like? Yes (1) | No   

RAMESH BOYA   9 years AGO

6 3 5 4 2
B C D E F

5 2 6 3 4
D F B C E

Like? Yes (1) | No   

pravallika   9 years AGO

according to their positions respectively,they wil be arranged as dfbce

Like? Yes (1) | No   

Kalpana   9 years AGO

6 and 5 are interchanged
2 and 3 are interchanged
then 3 and 4 are interchanged
accordingly letters position get changed

Like? Yes (1) | No   

nagamani   9 years AGO

Rearranging the letters as per the given sequence is done

Like? Yes (1) | No   

himank sood   9 years AGO

order
6 - 5 =3rd pos.
3 - 2 =5th pos
5 - 6 =1st pos
4 - 3 =2nd pos
2 - 4 =4th pos
among [b c d e f]

3rd is d
5th is f
1st is b
2nd is c and last is e

Like? Yes (1) | No   

GEETANJALI SHARMA   9 years AGO

because here 63542 and 52634 are the same no difference is that there position will change hence if we see accordingly there position of 63542 then its place is simply change in place of 6 into 5, 3 into 4, 5 into 6, 4 into 3 and 2 into 4. accordingly to given no we also can change the possition of the given letter B C D E F into D F B C E.

Like? Yes (1) | No   

Mugesh sivagnanam Krishnapillai   9 years AGO

Position of numbers initially
6- 1st ; 3-2nd ; 5-3rd ; 4-4th ; 2-5th =>63542
after changing
6-3rd;3-4th;5-1st;4-5th;2-2nd=>52634
Similarly interchanging BCDEF
B-3rd;C-4th;D-1st;E-5th;F-2nd=>DFBCE.

Like? Yes (1) | No   

Vidya Laxman Kokate   9 years AGO

According to given series of numbers and corresponding shift we can easily relate it to find the ans

Like? Yes (1) | No   

lavanya   9 years AGO

answer is DFBCE
bcz 6 3 5 4 2
5 2 6 3 4
change number positions..
now answer is DFBCE

Like? Yes (1) | No   

shivam dubey   9 years AGO

allot serial number : 6 3 5 4 2 B C D E F
1 2 3 4 5 1 2 3 4 5

but so in this case : 5 2 6 3 4 D F B C E
3 5 1 2 4 3 5 1 2 4

Like? Yes (1) | No   

kumaravel   9 years AGO

solution:
6 3 5 4 2 => 5 2 6 3 4
6 goes to 3rd position
3 goes to 4th position
5 goes to 1st position
4 goes to 5th position
2 goes to 2nd position
Similarly,
B C D E F => D F B C E

Like? Yes (1) | No   

Sourav Chatterjee   9 years AGO

given 63542=52634
if BCDEF=63542
Then
BCDEF=DFBCE

Like? Yes (1) | No   

sandeep prasad   9 years AGO

in the above expression

5->3rd position came at 2nd expression 1st position
similarly
d->in 3rd position comes in answer in 1st position

Like? Yes (1) | No   

Priya Verma   9 years AGO

replacing. .. mid one at 1st position.
last one at 2nd ,1st at 3rd , 2nd at 4th and 4th at the last position.

Like? Yes (1) | No   

harsha shenoy v   9 years AGO

pattern recognition, as in the first pattern the 3rd element comes first then comes 5th then 1st then the 2nd and finally the 4th element

Like? Yes (1) | No   

RAGUPATHI KANNAN   9 years AGO

rearrange the letters according to the number sequence... for ex: 6 is moved to 3rd position.. like that move B to 3rd position and do so.

Like? Yes (1) | No   

CHITHRA V K   9 years AGO

B C D E F
6 3 5 4 2
5 2 6 3 4
D F B C E

Like? Yes (1) | No   

Akanksha porwal   9 years AGO

digits of 63542 are interchanged and a new number is formed i.e.,52634 and DFBCE is formed
similarly BCDEF are interchanged as per the previous fromat

Like? Yes (1) | No   

ASHISH GUPTA   9 years AGO

6 3 5 4 2
5 2 6 3 4
B C D E F
D F B C E

Like? Yes (1) | No   

snehasis pramanik   9 years AGO

6 goes to middle so b goes in the mid and so on

Like? Yes (1) | No   

RISHABH JAIN   9 years AGO

as the position in sequence 63542 changed to 52634 similarly bringing the 3rd then 6th letter first i.e. d and f respectively.

Like? Yes (1) | No (1)  

18 Sep 2015 Train length

A train moving at 49 mph meets and is passed by a train moving at 63 mph. A passenger in the first train noted that the second train took 4.5 seconds to pass him. How long is the second train?

OPtion

1) 840 ft
2) 854.57 ft
3) 746.75 ft
4) 764.46 ft
5) 576.76 ft
6) 400 ft
7) 740.46 ft
8) 700 ft
9) 724 ft
10)None of these

Solution

162 5289 x (49 + 63) x 4.5
60 x 60
= 740.46 ft

Option 7)

Correct Option: 7 Best Solution (10)

Abhinav Akash   9 years AGO

The effective speed between the trains: 49 + 63 = 112 mph
Assume the passenger is stationary and the 2nd train is passing him at 112 mph.
1 mile= 5280 foot.
1 hour= 3600 secs.
(112*5280/3600)*4.5=739.5 ft.

Like? Yes (31) | No (6)  

AKASH   9 years AGO

The effective Relative speed between two trains is 49 + 63 = 112 mph
Now by Assuming that passenger is stationary and the 2nd train is passing him
at 112 mph than by
Finding the speed in ft/sec and multiplying it by 4.5
((112*5280)/3600)* 4.5 = 739.5 ft
HENCE THE ANSWER IS 740(approx) the length of the second train.

Like? Yes (4) | No (4)  

naveen   9 years AGO

LENTH of the train=((49+63)*5280*4.5)/3600
~740

Like? Yes (5) | No (5)  

SAGNIK DATTA   9 years AGO

((49+63)*(4.5/3600))*5280 miles

Like? Yes (2) | No (4)  

Kethineni Vinodh   9 years AGO

The effective speed between the trains: 49 + 63 = 112 mph
Assume the passenger is stationary and the 2nd train is passing him
at 112 mph
:
speed in ft/sec, mult by 4.5 sec: (112*0.44704m/s)*4.5sec
=739.5 ft is the length of the train

Like? Yes (4) | No (6)  

Arnab Maity   9 years AGO

The relative speed between the trains: 49 + 63 = 112 mph
Assume the passenger is stationary and the 2nd train is passing him
at 112 mph
Therefore, the length of the train = 112/3600*4.5 = 0.14m = 739.2 ft

Like? Yes (4) | No (6)  

SHAIK MAHABOOB BASHA   9 years AGO

from the problem we notice that the trains are travelling opposite to each other so relative speed of two trains are (49+63)112mph
we convert mph into feet per sec then we get 164.266666667 and then we multiply 4.5 secondswe get 739.2

Like? Yes (2) | No (5)  

anuj   9 years AGO

we have two trains moving in opposite direction...so,their speed will add. after that we need to find answer in feet so as we know in 1 mile=5280 feet.
convert the speed in feets per sec.Now we have speed and time ,just find the distance:)

Like? Yes (4) | No (7)  

gyanesh Patel    9 years AGO

1. If they trains are traveling away from each other he observes the train at a relative velocity of 112 mph (63 + 49) 2. To get the answer we must multiply the velocity times the time. 3. The hardest part about this problem are the units. 4. Convert mph to feet per sec, then multiply times 4.5 sec to get the answer in feet. Answer= 739.2 feet

Like? Yes (4) | No (7)  

praveendas   9 years AGO

x/112=4.5/3600.
we can get length in km.
convert it in t0 ft

Like? Yes (1) | No (6)  

17 Sep 2015 Find the number

The sum of 3 single digit numbers is 15 less than their product . If we subtract 2 from first given number then sum of these numbers will become 7 more than their product. The product of given 3 numbers will be?

OPtion

1) 6
2) 8
3) 12
4) 24
5) 30
6) 48
7) 60
8) 80
9) 100
10)120

Solution

If we subtract 2 from first given number then sum is 7 more than their product
So one of the number is 2. let remaining numbers are x and y
x + y +(2-2) =7
x+y = 7 (by second given condition)

& 2xy-(2+x+y) = 15 by first given condition

=> 2xy - x - y = 17
x = (17+y) / (2y-1)

possible solution of 2nd equation is x = 3 & y = 4, x = 4 & y= 3

and this satisfy equation 1
=> numbers are 2,3,4
product = 24

Correct Option: 4 Best Solution (57)

naveen   9 years AGO

let the numbers be x,y, z
x+y+z=xyz-15 & (x-2)+y+z=(x-2)yz+7
by solving them we get yz=12
the y, z may be 2,6 or 3,4:
but 3, 4 are satisfying the above condition from that we get x=2;
hence the product xyz=2*3*4=24
hence option (4) is correct

Like? Yes (14) | No (2)  

Anup Sahay   9 years AGO

if digits are 2,3,4 then their sum =9 and product =24 so the sum is 15 less than their product satisfies and if 2 is subtracted from 1st number the numbers are 0,3,4 so their sum = 7 and product =0 which satisfies the equation
so the product of numbers = 2*3*4=24
option 4)
i made a hit and trial here no equations which took me less time

Like? Yes (6) | No   

ABHINAV PUSHPAM   9 years AGO

The required number is 243

Like? Yes (7) | No (4)  

shibanti sanyal   9 years AGO

the two equations will be: x+y+z=xyz-15 & (x-2)+y+z=(x-2)yz+7.
Solving we get yz=12 & x=2.
Hence, product=2*12=24. ans

Like? Yes (3) | No   

kriti kankariya   9 years AGO

let the three numbers be x,y,z
then,x+y+z=x*y*z - 15
& (x-2)+y+z=(x-2)*y*z + 7
solving these we will get y*z=12
possiblities are {1,12} , {2,6} , {3,4}
taking these {3,4} is satisfying the conditions giving x=2
so x*y*z=2*12=24

Like? Yes (2) | No   

Anubrindha   9 years AGO

24 = 4*3*2
Sum of 4+3+2=9
Sum of these 3 numbers are 15 less than their product

Like? Yes (2) | No   

rahul shaw   9 years AGO

since diff in 1st case is 15 so the value of product should be above 15...
then we came to 24 and then breaking it into factors and calculating...we can get it...
24=4*3*2
sum=9
9+15=24
so option 4

Like? Yes (2) | No   

bhaskar   9 years AGO

xyz=x+y+z+15
(x-2)yz+7=x+y+z-2
yz=12
y=3
z=4
(y=2,z=6 is not possible for both the conditions)
12x=x+22
x=2
product =2*3*4=24

Like? Yes (2) | No (1)  

rajat gupta   9 years AGO

since numbers are 2, 3 and 4 this is the only possible case by hit and trial method

Like? Yes (1) | No   

Arvind kumar   9 years AGO

Product of 2,3 and 4 is 24 which is 15 more than their sum i.e.9

Like? Yes (3) | No (2)  

Deepak Agarwal   9 years AGO

the three digit no. is 234
where 2+3+4=9 & 2*3*4=24 which is 15 more than their sum.
If we subtract 2 from 2 we get 0 so their product will be zero and sum will be 0+3+4=7.
So the product is 2*3*4=24

Like? Yes (1) | No   

Rohit Agrawal   9 years AGO

x+y+z=xyz-15
x+y+z-2=(x-2)yz+7
=>yz=12
y=2or 3 z=6 or 4
3 4 holds for the 1st equatiion
solving x=2
answr is 2x3x4=24

Like? Yes (1) | No   

sudiptaa   9 years AGO

numbers are 2,3,4
Product is 2*3*4 = 24

Like? Yes (1) | No   

praveendas   9 years AGO

three digits are 4,3,2.no is 432..verify it with given conditions

Like? Yes (1) | No   

Mayur jaiswal   9 years AGO

2*3*4=24
Dat is 15 less Dan 2+3+4=9

Like? Yes (1) | No   

siddhi datri   9 years AGO

a+b+c=abc-15
a+b+c-2=abc+7
on solving them, we get
ab=12,then abc=24 satifies the both equation.

Like? Yes (1) | No   

Kethineni Vinodh   9 years AGO

4+3+2=9
4*3*2=24
432-2=430 i.,e 4+3+0=7
4*3*0=0

Like? Yes (1) | No   

Subhendu Pradhan   9 years AGO

a*b*c=15+a+b+c
(a-2)+b+c=7+(a-2)*b*c=7+abc-2bc
bc=12
abc will be multiple of 12
so,b & c may be 4 and 3 respectively
by putting the value of a=1,2,3.... u have to check the 1st or 2nd condition u will find the option

Like? Yes (1) | No   

prasad   9 years AGO

nm

Like? Yes (1) | No   

ADARSH GAURAV   9 years AGO

24 is the answer.........

Like? Yes (1) | No   

Ankit singh   9 years AGO

24

Like? Yes (1) | No   

DURGESH KUMAR   9 years AGO

24=4*3*2 and sum =9, 24-9 =15

Like? Yes (1) | No   

nirmal das   9 years AGO

the numbers are 2,3,4...as 2+3+4=9 and 2*3*4=24 which is 15 more than their sum...when 2-2=0 then product is 0 bt sum is 7....

Like? Yes (1) | No   

Shankar   9 years AGO

a b c=abc-15
(a-2) b c=7 (a-2)bc
Solving we get
bc=6
Then put bc=6 in first equation
a b c=6a-15
b c 15=5a
bc=6,therefore chances for b and c is 6,1 or 2,3
We take 2,3
Thus a=4
Now abc =4*2*3=24

Like? Yes (1) | No   

rakesh sharma   9 years AGO

15+x+y+z=xyz.....(1)
(x-2)+y+z=(x-2)yz+7...(2)

solve both equ. then we find yz=12
xyz=?
12x=?
by answer:
x=1,2,4,5
put x=2
xyz=24
x+y+z=xyz-15 by equ. (1)
x+y+z=24-15=9
so
x+y+z=9
x=2,y=4/3,z=3/4

so answer (4) is correct
xyz=24

Like? Yes (1) | No   

Anshul khandelwal   9 years AGO

a+b+c+15=a*b*c ----(a)
(a-2)+b+c=(a-2)*b*c -----(b)

solving both equation a and b above
bc=12
so value of b and c will either be 4 and 3 or 6 and 2 or 1 and 12.
best suitable value is 4 and 3 because on solving with other value value of a i not coming integral.
so from first equation (a)
a+4+3+15=12a
a=2

hence multiplication of abc = 24

Like? Yes (1) | No   

CHANDAN KUMAR   9 years AGO

let 3 single digit no. be x , y and z.
now,
x+y+z = xyz -15 ......(I)

(x-2)+y+z = (x-2)(yz) + 7
or , x+y+z = xyz -2yz + 9...... (ii)

solving equations I and ii , we get

xyz-15 =xyz-2yz +9
or,
2yz = 24
or,
yz = 12......... (iii)

let y = 3 & z =4 ( from equation iii )

now , equation (I) become
x+3+4 = 12x -15
or,
x+7 =12x -15

or,
11x = 22
or,
x = 2


finally ,
3 digits are
2 ,3, 4 .

so, their product = 2�3�4 =24

correct answer
options 4) 24

Like? Yes (1) | No   

pawan kumar   9 years AGO

a+b+c+15=a*b*c--- (1)
(a-2)+b+c=(a-2)*b*c+7---(2)
solving 2 equations we get ,b*c=12
taking b=3 & c=4 or b=4 & c=3 we get a=2
hence a*b*c=24,

Like? Yes (1) | No   

saurabh kumar   9 years AGO

digit will be 4,3,2
4+3+2=9
4*3*2=24
diff=15
2-2=0
0+3+4=7
4*3*0=0
diff=7

Like? Yes (1) | No   

Mayank Aditya   9 years AGO

Let no. are x,y and z.
x+y+z+15=xyz.....Eqn. 1
x-2+y+z=(x-2)yz+7....Eqn. 2
From Eqn. 1 and Eqn. 2
yz=2
so the possible conditions may be
1) y=2 and z=6(it is false because then x can't be a single digit no.)
2) y=3 and z=4(then x=2)
so, xyz=2*3*4=24

Like? Yes (1) | No   

Aakashdeep Madaan   9 years AGO

let three numbers be a,b,c then:
a+b+c=abc-15 and (a-2)+b+c=7+(a-2)bc
and after solving these two equations we get the value of bc=12
now, there could only be two possible values for b and c in this case which are 3,4 or 6,12 as the numbers are only single digit numbers
now, let b=3 , c=4 then put these values in equation1 and find the value of a as 2
but when we put b=6 c=2 then we get a as a decimal number , so we ignore that case
hence, a=2 b=3 c=4
and their product is 2*3*4=24

Like? Yes (1) | No   

Pesari Udayasree   9 years AGO

let x,y,z are the no.'s
then given x+y+z=xyz-15 and (x-2)+y+2=(x-2)yz+7
by trail and error x,y,z are 2,3,4
therefore 2*3*4=24

Like? Yes (1) | No   

vivek   9 years AGO

432 is the no.
so 4+3+2=9 and 4*3*2=24
so, product - sum =15
now, subtract 2 from the number, we get
430
sum of new no. 4+3+0=7
product of new no.= 4*3*0=0
so sum of the new no. is 7 more than product of the no.
hence, required product of given no. is 24

Like? Yes (2) | No (1)  

Moutam Vishnu Murthy   9 years AGO

Ans: 24 (2*3*4)
As (2*3*4)-15=2+3+4
(2-2)*3*4=0

Like? Yes (1) | No   

Deepanshu Chaturvedi   9 years AGO

the equation is valid for digits 2,3,4. therefore, product of digits is 24.

Like? Yes (1) | No   

Parthasarathi.S   9 years AGO

(2+3+4)+15=2*3*4=24
(0+3+4)-7=0*3*4=0
xyz=24

Like? Yes (1) | No   

Rahul Hirve   9 years AGO

X=2,
yz=12;
y=3,
z=4;

Like? Yes (1) | No   

vaibhavi lodhiya   9 years AGO

2*3*4=12,
& 2+3+4=9
24-9=15

Like? Yes (1) | No   

AARTI OJHA   9 years AGO

product of 2 nos is 12
so the product of 3 nos must be a multiple of 12
after solving we are getting the first no as 2
thus, the answer is 24

Like? Yes (1) | No   

Shrey Agrawal   9 years AGO

X+y+z=xyz-15....(1)
X-2+y+z=(x-2)yz+7....(2)
Substituting value of equation (1) in eqn(2)
Yz=12
Now..since x,y and z are single digit number.therefore possible combinations for y*z are 4*3 or 6*2...
Taking first possibility and substituting the value in eqn(1)..weget x=2.
Hence x*y*z=24

Like? Yes (1) | No   

sumit kumar   9 years AGO

let no is a,b and c.
a/c to question a+b+c=abc-15
a+b+c-abc=-15 ........(1)
(a-2)+b+c-(a-2)bc=7
a+b+c-2-abc+2bc=7
a+b+c-abc+2bc=9 .........(2)
from eq. (1) and (2)
bc=12=4*3
b=4,c=3
put the value in eq. (2)
a+4+3-12a+24=9
-11a=9-31=-22
a=2
prouct of no is abc=24

Like? Yes (1) | No   

vikash kumar das   9 years AGO

As, x+y+z=xyz-15 ......(i)
now in second case if we subtract 2 from the first no x then a/q
(x-2)+y+z=(x-2)yz+7 ...(ii)
On solving (i) nd (ii) we get yz=12
since x,y and z are single digit
therefore value of y and z should be (3,4),(4,3),(6,2),(2,6)
if we put y=3 and z=4 in eqn-(i) we get x=2 as single digit while (6,2) doesn't satisfy both eqn.
therefore the product is 2*3*4=24.

Like? Yes (1) | No   

Kalpana   9 years AGO

the numbers are 2,3,4
2 is the first number when subtracted it gives 4+3=7
so their product is 24

Like? Yes (1) | No   

Ankush dhadwal   9 years AGO

here yz=12after solving the two equation.then next step is to use hit and trail by assuming values to be 4&3 or 6&2.then substituting the both value onr by one and at last u will find that one with 4&3 on substituting we will get x=2

Like? Yes (1) | No   

SK INTAJ MOHAMMAD   9 years AGO

x+y+z=xyz-15.....(1)
and (x-2)+y+z=(x-2)yz+7;.......(2)
solving two equations we get yz=6;
here 6 is possible if y=2,z=3 or y=3, z=2;
puttting these above values in the equation (1) we get x=4;
so xyz=x*yz=4*6=24...... ans(4)..

Like? Yes (1) | No   

Aman   9 years AGO

From the question we know
X+Y+Z=X*Y*Z-15
and
(X-2)+Y+Z=(X-2)*Y*Z+7
now
on solving we get
Y*Z=12
so
either
4*3 is Y*Z
OR
6*2 is Y*Z
now 6*2 is not possible because it does't satisfies second equation so
4*3*2 is X*Y*Z
SO
24 IS THE X*Y*Z

Like? Yes (1) | No   

himanshu jaiswal   9 years AGO

let 3 no be x ,y,z
x+y+z=xyz-15
(x-2)+y+z=xyz+7
from here yz=12
if y=4 z=3
then we have x=2 which satisfy both the equation
so the product=2*4*3=24

Like? Yes (1) | No   

Ashish Kumar Singh   9 years AGO

let's assume three single digit number is x y z
given that (x+y+z)+15=xyz
and ((x-2)+y+z)-7=xyz
For Example if x=2,y=3,and z=4
then 9+15=24
and (0+3+4)-7=0
so the product of these single digit number is 24

Like? Yes (1) | No   

TONI PRIYA   9 years AGO

X*Y*Z=X+Y+Z+15
(X-2)*Y*Z+7=(X-2)+Y+Z
From these 2 eq. we get y*z=12
by hit and trial we conclude that y=3,z=4
after that when we put x=2 then it satisfy the 2 eq.

Like? Yes (1) | No   

Poornima Bharadvaj   9 years AGO

let the nos be 2,3,4 and their sum is 9 and product is 24 and it is 15 lessthan thier product and product of 3 num is 24

Like? Yes (1) | No   

ramniwas   9 years AGO

the numbers are 2,3,4
1 condition : sum=product-15
i.e 2+3+4=2*3*4-15 => 9=24-15 => 9=9
2 condition : subtract two from first i.e 2-2 =0
sum=product+7
0+3+4=0*3*4+7
7=7
TRUE
since ANS will be 2*3*4 =24

Like? Yes (1) | No   

Amit chaturvedi   9 years AGO

digits are 2,3,4 which proves both case, here we will consider 2 as a first number
2+3+4=9 and 2*3*4=24
sum is 15 less than their product
and
0+3+4=7 and 0*3*4=0
sum is 7 more than their product

Like? Yes (1) | No   

premchand meena   9 years AGO

x+y+z =xyz-15
(x-2)+y+z= (x-2)yz+7
solve both equ..
we get
yz = 12
so x+ y+z= 12x- 15
11x = y+z+15
so we know y+z+15 is multiple of 11
22, 33 ,44
possible y, z
12, 1
6,2
3,4
4,3
2,6
1, 12
takes which setisfy the equation
y+z = 7
so x = 0

Like? Yes (1) | No   

priyanka burnwal   9 years AGO

factor of 24 is 2,3,4
product of 2,3,4=24
and their sum is 9
and when 2 is substracted from 1st digit
sum =7
and product =0

Like? Yes (1) | No   

SAGNIK DATTA   9 years AGO

the given numbers are 2,3 and 4 and all the conditions are satisfied

Like? Yes (2) | No (2)  

UDIT   9 years AGO

24=2x3x4
24-(2+3+4)
24-9=15
here, sum is 15 less than product of three numbers
2 is decreased from 2 i.e.2-2=0
thus, 0x3x4=0
and the new sum is 0+3+4=7
so sum is greater than product by 7.
so product of three numbers is 24(option 4)

Like? Yes (1) | No (1)  

aman aditya   9 years AGO

three numbers are 4,3,2

Like? Yes (1) | No (1)  

16 Sep 2015 Measure the area

A rectangular photograph is placed in a frame that forms a border two inches wide on all sides of the photograph. The photograph measures 8 inches high and 10 inches wide. What is the area of the border, in square inches?

OPtion

1) 20
2) 24
3) 28
4) 36
5) 40
6) 64
7) 72
8) 76
9) 88
10) none of these

Solution

Give the photograph area is 8X10
So totral frame area will be
(8+2+2) X (10+2+2)
= 12 X 14
Frame area = 168
Photograph area = 80
Border area = 168 - 80
88

Correct Option: 9 Best Solution (75)

ABHINAV PUSHPAM   9 years AGO

In order to find the area of the frame, we need to subtract the area of the photograph from the area of the photograph and the frame together.
The area of the photograph is 8*10= 80 square inches. The height of the whole frame (including the photograph) would be 8+2+2 = 12,
and the width of the whole frame, 10+2+2 = 14.
Therefore, the area of the whole figure would be 12 * 14 = 168 sq. inches.
Subtracting the area of the photograph from the area of both the frame and photograph,
we find the answer to be 168-80 = 88
Option 9)

Like? Yes (10) | No (4)  

anandhi   9 years AGO

border width and length will be 4 inches greater than photo. so, (12*14)-(8*10)=88

Like? Yes (3) | No (1)  

SUMIT PAREEK   9 years AGO

length of photo=8inch
width of photo =10inch
Area of photo=8*10 sq inch=88 sq inch
Now ,
in frame 2 inch border along all the sides
so,length of frame=12inch
width of frame=14inch
Area of frame =12*14 sq inch=168 sq inch
so, Area of border= (168-80) sq inch=88 sq inch

Like? Yes (4) | No (2)  

siddhi datri   9 years AGO

area=2*14*2+2*8*2=56+32=88

Like? Yes (4) | No (2)  

abhishek   9 years AGO

14*12-10*8=88

Like? Yes (5) | No (3)  

vikash kumar   9 years AGO

area of the frame = (8+2+2)*(10+2+2) =168
area of the photograph = 10*8 = 80
so,area of the border = 168 - 80 = 88

Like? Yes (1) | No   

sudiptaa   9 years AGO

Area of photo= 10*8 = 80 sq inches
Area of frame with photo = 12*14 = 168 sq inches
Area of border = 168-80=88 sq inches

Like? Yes (1) | No   

S.Hemanth kumar   9 years AGO

actual area =10x8=80
total frame area=wide+4xhigh+4=168
area of broder=168-80=88

Like? Yes (1) | No   

gouselazam   9 years AGO

height=8in,width=10inch
area of border=(10*2)*2+(12*2)*2=88inch-square

Like? Yes (1) | No   

Janhavi   9 years AGO

case 1: photograph
length=8 breadth=10
area =length*breadth
area1 =8*10=80

case 2: photograph + frame
new length =8 +2+2 =12
new breadth = 10+2+2=14
area =length*breadth
area2=12*14=(4*3)*(2*7)=8*21

area of border = area2-area1
= 8*21- 80
= 8*(21-10)
= 88

So, option : 9

Like? Yes (2) | No (1)  

Geethanjali   9 years AGO

by using formula area=2w(l+b+2w)

Like? Yes (1) | No   

ezhilane   9 years AGO

area of the photograph is 8*10 = 80 square inches.
height of the whole frame would be 8+2+2 = 12.
width of the whole frame, 10+2+2 = 14.
area of the whole figure= 12 * 14 = 168 square inches.
the area of the photograph from the area of both the frame and photograph=168-80=88.

Like? Yes (1) | No   

SK INTAJ MOHAMMAD   9 years AGO

Total area =14*12=168
area of photograph=8*10=80
so,area of the border=(168-80)=88. ans(9)

Like? Yes (1) | No   

Subhendu Pradhan   9 years AGO

14*12=168,8*10=80,
168-80=88

Like? Yes (1) | No   

akshay jain   9 years AGO

10 inch width becomes 14 inches on including border
now border length is 14 inch and width is 2 inch so are become (14*2) 28 similarly on other side and calculataing same on length side we get 88

Like? Yes (1) | No   

momin ashraf ahamed   9 years AGO

area of frame wid photographminus area of photograph

Like? Yes (1) | No   

Thejaswi Pericharla   9 years AGO

area of frame is 10 *8 which is 80
area of rectangle is 14 *12 which is 168
subtract and get 88

Like? Yes (1) | No   

kartheek   9 years AGO

10 +4 = 14
8 + 4 = 12
14* 12 = 168
10 *8 =80
168-80=88

Like? Yes (1) | No   

Sandip Shaw   9 years AGO

height wise area=2*(2*8)=32
width wise area=2*(2*10)=40
area of the corner sqrs=4*(2*2)=16
total Area=32+40+16=88

Like? Yes (1) | No   

shreya kolay   9 years AGO

simple calculation
12*14-8*10

Like? Yes (1) | No   

Surabhi Yadav   9 years AGO

Area of photograph+border=h*b
h=2+8+2=12inches
b=2+10+2=14
=12*14=168 square inches
area of photograph=8*10=80
therefore
Area of border=(area of photograph+border)-(area of photograph)
=168-80
=88square inches

Like? Yes (1) | No   

ramya   9 years AGO

In order to find the area of the frame, we need to subtract the area of the photograph from the area of the photograph and the frame together. The area of the photograph is $8 times 10 = 80$ square inches. The height of the whole frame (including the photograph) would be $8+2+2 = 12$, and the width of the whole frame, $10+2+2 = 14$. Therefore, the area of the whole figure would be $12 times 14 = 168$ square inches. Subtracting the area of the photograph from the area of both the frame and photograph, we find the answer to be $168-80 = 88

Like? Yes (1) | No   

Tushar Sharma   9 years AGO

Area of frame=14*12
i.e. (10+2+2)*(8+2+2)
Area of photograph=10*8
Area of border=Area of frame - Area of photograph

Like? Yes (1) | No   

sumit kumar   9 years AGO

With border width and height of the photograph is respectively 10+2*2=14 and 8+2*2=12 .
Area of photograph with border is 14*12=168
Area of photograph is 8*10=80
so area of border is 168-80=88

Like? Yes (1) | No   

Parthasarathi.S   9 years AGO

A(photo)
10*8=80
A(frame nd foto)
14*12=168
A(frame)
168-80=88

Like? Yes (1) | No   

Ishy   9 years AGO

Its simple calculate the area of bigger rectangle having height (8+2+2) * width (12+2+2) and subtract from it the area of smaller rectangle having hwidth (8) * width (10)= 168-80= 88

Like? Yes (1) | No   

Vinit Patil   9 years AGO

length and breath of photo is 8 and 10 respect, So area =80
l and B of frame is 12 and 14, so area=168
And 168-80=88

Like? Yes (1) | No   

vijay krishna reddy   9 years AGO

area of rectangular photograph with frame is 168
area of rectangular photograph is 80
area of border=168-80=88

Like? Yes (1) | No   

Arvind kumar   9 years AGO

Area of photograph with border=(8+4)*(10+4)
i.e. 168
Area of photograph=8*10
i.e. 80
Area of border =168-80
i.e.88 square inch

Like? Yes (1) | No   

RAJ KUMAR   9 years AGO

In order to find the area of the frame, we need to subtract the area of the photograph from the area of the photograph and the frame together. The area of the photograph is $8 times 10 = 80$ square inches. The height of the whole frame (including the photograph) would be $8+2+2 = 12$, and the width of the whole frame, $10+2+2 = 14$. Therefore, the area of the whole figure would be $12 times 14 = 168$ square inches. Subtracting the area of the photograph from the area of both the frame and photograph, we find the answer to be 168-80 = 88

Like? Yes (1) | No   

Shammi Pandey   9 years AGO

=(area of frame-area of fotographs)

l engh tof frame=14 lenght of fotograph =8
breath of frame =12 breath of fotograph=10

=(14*12-10*8)
=168-80
=88sqinches

Like? Yes (1) | No   

Aman Gaurav   9 years AGO

In order to find the area of the frame, we need to subtract the area of the photograph from the area of the photograph and the frame together. The area of the photograph is 8*10=80
The height of the whole frame (including the photograph) would be 8+2+2=12
and the width of the whole frame, 10+2+2=14
Therefore, the area of the whole figure would be 12*14=168
Subtracting the area of the photograph from the area of both the frame and photograph, we find the answer to be 168-80=88

Like? Yes (1) | No   

shreeprakash   9 years AGO

since big rectangle - small rectangle
L*W-l*w
where L=l+2+2 and W=w+2+2
14*12-8*10
= 88 ans.

Like? Yes (1) | No   

Aman   9 years AGO

In order to find the area of the frame, we need to subtract the area of the photograph from the area of the photograph and the frame together. The area of the photograph is 8*10=80
The height of the whole frame (including the photograph) would be 8+2+2=12
and the width of the whole frame, 10+2+2=14
Therefore, the area of the whole figure would be 12*14=168
Subtracting the area of the photograph from the area of both the frame and photograph, we find the answer to be 168-80=88

Like? Yes (1) | No   

saikumar   9 years AGO

we need to calculate total area of frame and subtract it from area of photo..then we get the area of the border...
area of the frame=14*12=168
area of photo=10*8=80
area of the border=168-80=88

Like? Yes (1) | No   

naveen   9 years AGO

outer rectangle area=12*14
lower rectangle area=10*8
the area of border=168-80=88

Like? Yes (1) | No   

Mugesh sivagnanam Krishnapillai   9 years AGO

Area of photograph= 10x8=80sq.in
Area of frame=14x12= 168 sq.in
Area of border = Area of frame-area of photograph
=168-80
=88sq.in

Like? Yes (1) | No   

Harsh Saxena   9 years AGO

Area of innner rectangle = 8+10 = 80 sq inch.
Area of outer = (10+2+2) * (8+2+2) = 168
So area of border = 168 - 80 = 88

Like? Yes (1) | No   

Akram Raza   9 years AGO

Area of photograph with border = 12 * 14 = 168 sq inches
Area of photograph without border = 8 * 10= 80 sq inches

area of border = 168 - 80 = 88 sq inches

Like? Yes (1) | No   

rohit kumar jain   9 years AGO

area of photograph=10*8=80 inches
dimension of photograph after including the frame=14*12=188
total area of border=188-80=88

Like? Yes (1) | No   

anubhav kumar   9 years AGO

total height=10+2+2=14
total width =8+2+2=12
area=14*12=168
area of photo=10*8=80
area of border =168-80=88

Like? Yes (1) | No   

Amit chaturvedi   9 years AGO

Area of Photograph which is a Rectangle=Length*Width
8*10=80,
Now Length of the whole frame including photograph=8+2+2=12
and Width of the whole frame including photograph=10+2+2=14
Area of (Border + Photograph)=12*14=168,
Area of (Border+Photograph) - Area of Photograph=Area of Border.
168-80=88

Like? Yes (2) | No (2)  

Rupkatha Banerjee   9 years AGO

8+2+2=12
10+2+2=14
12*14=168
168-(8*10)=88

Like? Yes (1) | No (1)  

TAUSEEF AMEEN   9 years AGO

Area of Frame=(10+4)*(8+4)
=168 square inch
Area of Photograph=(10)*(8)
=80 square inch
Area of Border=Area of frame-Area of Photograph
=168-80
=88 square inch
hence option 9 is correct

Like? Yes (1) | No (1)  

SAGNIK DATTA   9 years AGO

since 2 inches wide so (12*14)-(8*10)

Like? Yes (1) | No (1)  

SHAIK MAHABOOB BASHA   9 years AGO

total area of the (frame+photograph)=168
area of the photograph=80
total area of the border=168-80
=88

Like? Yes (1) | No (1)  

praveendas   9 years AGO

area of the border in inches^2is ==length*breadth
length is(10+10+12+12)
breadth is 2 common
area is88 inches^2
or
area of the frame including photo-area of the photo=area of the frame..
area of frame=12*14=168
area of the photo=8*10=80
168-80=88

Like? Yes (1) | No (1)  

pavandeep singh ubbi   9 years AGO

area of full frame- area of photo

Like? Yes (1) | No (1)  

Pesari Udayasree   9 years AGO

area of the photograph is 8*10=80 square inches
area of total frame is 12*14=168 square inches
since 8+2+2=12 and 10+2+2=14
therefore area of border is168-80=88

Like? Yes (1) | No (1)  

Abhinav Akash   9 years AGO

Area of whole frame +Photograph=(8+2+2)*(10+2+2)=168 sq.inch
Area of photograph=10*8=80
So, Area of Frame= Area of whole - Area of Photograph
168-80=88 So option 9 is correct.

Like? Yes (1) | No (1)  

MANUPOTI ANAND   9 years AGO

Frame area=14*12
=168
Photograph area=8*10
=80
Border area=168-80
=88

Like? Yes (1) | No (1)  

Anup Sahay   9 years AGO

area of photo= 8*10=80 sq inches
to get area of photo with frame add 2 and 2 inches i.e. 4 inches on both sides
so l=10+2+2=14 inches and b=8+2+2=12 inches
it's area=14*12=168
so are of border=area of photo with frame-area of photo
= 168-80=88
option 9) 88 is answer

Like? Yes (2) | No (2)  

akanksha    9 years AGO

whole frame area=(14*12)= 168
photograph area=(10*8)=80
border area=168-80=88

Like? Yes (1) | No (1)  

diksha   9 years AGO

length of rectangle along with frame=8+2+2=12
breadth of rectangle along with frame=10+2+2=14
area=12*14=168
area of photograph=10*8=80
area of border=88

Like? Yes (1) | No (1)  

YOGESHWAR KUMAR   9 years AGO

The total area of photo is H*W = 10*8 = 80 inches
increase 2 inches in all sides so H = 10+4 = 14 inches
and W = 8+4 = 12 inches
Now Area of Frame is H*W = 14 * 12 = 168
Now the Area of border = Area of frame - Area of Photo
= 168 - 80
= 88

Like? Yes (1) | No (1)  

bhaskar   9 years AGO

dimensions with frame 14,12
area of frame (14*12)-(10*8)=88

Like? Yes (1) | No (1)  

Anurag Sahay Sriavsatav   9 years AGO

2 inches border on all side so actual length and bredth of the frame is:
length=8+2+2=12
bredth=10+2+2=14
Area= 12*14=168
Now area of the pic is:
10*8=80
Now area of the border is : 168-80=88
so option 9 is correct.

Like? Yes (2) | No (2)  

SOURABH   9 years AGO

area of photo=8*10=80
area of whole area=12*14=168
area of border=168-80=88

Like? Yes (1) | No (1)  

MADHUBABU   9 years AGO

area of photograph=(8*10)=80
width of whole frame(including photograph)=(10+2+2)=14
height of whole frame=(8+2+2)=12
area of whole frame=(12*14)=168
therfore
area of the border=area of whole frame-area of photograph
=168-80
= 88

Like? Yes (2) | No (2)  

Anshul khandelwal   9 years AGO

Area of upper and lower border = (8*2)+(8*2) = 32
Area of both side border = ((2+2+10)*2)+((2+2+10)*2) = 56
total area= 32+56 = 88

Like? Yes (2) | No (2)  

Chandrajeet Yadav   9 years AGO

{(10+2+2)*(8+2+2)} - (10*8)
=(14*12)-(10*8)
=168-80
=88

Like? Yes (1) | No (1)  

HEMANT KUMAR   9 years AGO

high will be= 8+2+2= 12 inches
width will be=10+2+2=14 inches
total area of border= (area of total frame)-(area of photograph)
= (12 x 14)-(8 x 10)
=88 sq. inches (ans.)

Like? Yes (1) | No (1)  

Kethineni Vinodh   9 years AGO

area of frame=14*12=168
area of photo=10*8=80
area of border=168-80=88 sq.inches

Like? Yes (1) | No (1)  

Shashank Gupta   9 years AGO

area of photograph=10*8=80
and
area of frame = (10+2+2)*(8+2+2)=168
area of border= area of frame - area of photograph =168-80=88(ans)

Like? Yes (1) | No (1)  

himank sood   9 years AGO

total area = 14*12 =168
area of photograph= 8*10= 80
area of border =168-80= 88

Like? Yes (1) | No (1)  

Ajay Kumar Gupta   9 years AGO

The width is 4 inches longer than the photo's width. Same for length. So, the entire "setting" is 12 inches by 14 inches and the photo is 8 inches by 10 inches. So, the area of the frame in sq. in. is:
12*14-8*10=168-80=88

Like? Yes (1) | No (1)  

Rahul Khatavkar   9 years AGO

12*14=168
-
10*8 = 80
-------------------
=88

Like? Yes (1) | No (1)  

Ramesh Sriram   9 years AGO

12*14-10*8=88 sq inches

Like? Yes (1) | No (1)  

Sandeep Kumar   9 years AGO

8 2 2 = 12
10 2 2= 14
Required area = 12x14 - 10x8
= 88

Like? Yes (1) | No (1)  

Amarnath Moorthy   9 years AGO

The height of the whole frame would be 8+2+2 = 12, and the width of the whole frame, 10+2+2 = 14 Therefore, the area of the whole figure would be 12 times 14 = 168 square inches. Subtracting the area of the photograph from the area of both the frame and photograph, we find the answer to be 68-80 =

Like? Yes (1) | No (1)  

Deepak Kumar   9 years AGO

12*14=168
168-(10*8)=88

Like? Yes (1) | No (1)  

Arpan Ganguly   9 years AGO

area of photograph = 8*10 = 80
area of photograph+border = (8+2+2)*(10+2+2)=168
so area of border = 168-80=88 option 9) correct

Like? Yes (1) | No (1)  

Dhanraj Wanjare   9 years AGO

Area of Rectangular photograph is = Length * Width;
.......................................................... = 10 * 8;
.......................................................... = 80;

and Area of Rectangular fram with photograph is: = l*w;
......................................................................... = (10+4)*(8+4)
........................................................................... = 168;

area of fram = (total area of fram with photograph) -
( area of photograph );
....................... = 168 - 80;
....................... = 88;
so option 9 is satisfied ;

Like? Yes (1) | No (1)  

Shyamnks    9 years AGO

In order to find the area of the frame, we need to subtract the area of the photograph from the area of the photograph and the frame together. The area of the photograph is 8 times 10 = 80 square inches. The height of the whole frame (including the photograph) would be 8+2+2 = 12, and the width of the whole frame, 10+2+2 = 14. Therefore, the area of the whole figure would be 12 times 14 = 168 square inches. Subtracting the area of the photograph from the area of both the frame and photograph, we find the answer to be 168-80=88

Like? Yes (1) | No (2)  

Homenath   9 years AGO

In order to find the area of the frame, we need to subtract the area of the photograph from the area of the photograph and the frame together. The area of the photograph is 8 times 10 = 80 square inches. The height of the whole frame (including the photograph) would be 8+2+2 = 12, and the width of the whole frame, 10+2+2 = 14. Therefore, the area of the whole figure would be 12 times 14 = 168 square inches. Subtracting the area of the photograph from the area of both the frame and photograph, we find the answer to be 168-80=88

Like? Yes (1) | No (2)  

15 Sep 2015 Value of T

S varies directly as R varies and T varies inversely as R varies. At a time R = 20, S = 40 and T = 10. If R is changed to 10, then the value of T will be

OPtion

1) 20
2) 10
3) 30
4) 40
5) 80
6) 120
7) 60
8) 100
9) 70
10)None of these

Solution

S -> R
T -> 1/R
So S = k1 R and T = k2/R
When R = 20, S = 40, T = 10 we have k1 = 2 and k2 = 200
Therefore
S = 2R and T = 200/R
When R = 10, then T = 200/10 = 20

Option 1)

Correct Option: 1 Best Solution (111)

Shashank Gupta   9 years AGO

S=k*R
1/T=k*R
=>S/T=k*R
40/10=k*20
k=1/5

When Value gets changed
40/T=1/5*10
Hence T=20

Like? Yes (7) | No (2)  

PRAGATHI G   9 years AGO

when R is changed to 10. implies R decreases by 10. since T varies inversely to R. T should get increased by 10. that's 20

Like? Yes (4) | No (1)  

adarsh   9 years AGO

t varies inversely to r then so t= 20

Like? Yes (3) | No   

Mugesh sivagnanam Krishnapillai   9 years AGO

The multiplication factor between S,T & R is 2
Since R and T are inversely propostional.,
T=10x 2=20.

Like? Yes (3) | No   

kriti kankariya   9 years AGO

as given T is inversly prop. to R
at first R=20 , T=10
now, R=10 i.e. 1/2 of previous
so T will be doubled, T = 20

Like? Yes (5) | No (3)  

jayaram   9 years AGO

here T and R are inversely praportional.then here R is decreased to 10 implaise T is increased to 20

Like? Yes (2) | No   

KALA BHANU PRAKASH   9 years AGO

If R=20 then T=10&
If R=10 then T=20.

Like? Yes (2) | No   

R.DIVYA    9 years AGO

R value is reduced to half i.e 10. Since S is directly proportional to R, its value is also reduced half i.e 20. Since T is inversely proportional to R, its value is increased to half i.e 20.

Like? Yes (2) | No   

sandeep prasad   9 years AGO

if R=20 and T varies inversely as R varies so if R=10 then T=2*intial T...=10*2=20

Like? Yes (2) | No   

swati sharma   9 years AGO

R/S=20/40 = 1/2
S.T=K WHERE, K is a constant =>(40).(10)=K
WHEN R=10, => S=20
ST=K=400
20*T=400
=>T=20

Like? Yes (2) | No   

Abhinandan mahato   9 years AGO

r is half therefore t will be double that is 20

Like? Yes (2) | No   

priyanka burnwal   9 years AGO

accod. to ques
let x be variable
s=rx so x=40/20=2
t=x/r
so x=200
t=200/r
t=200/10=20

Like? Yes (3) | No (1)  

gouselazam   9 years AGO

T1R1=T2R2
(10*20)/10=20

Like? Yes (2) | No (1)  

rahul shaw   9 years AGO

R=x/T
R=20 AND T=10
x=200
WHEN R=10 THEN T=20
So option 1

Like? Yes (2) | No (1)  

vikash kumar   9 years AGO

10=k/20.
k=200.
now t=k/r
t=200/10
=20

Like? Yes (1) | No   

Aman Gaurav   9 years AGO

we know that S is directly varies with R and inversely varies with T
so,
if R become half then S also become Half and T become Twice
.
so T = 20

Like? Yes (1) | No   

Aman   9 years AGO

we know that S is directly varies with R and inversely varies with T
so,
if R become half then S also become Half and T become Twice
.
so T = 20

Like? Yes (1) | No   

Harsh Saxena   9 years AGO

There can be 2 ways:
R = K/T
R=20, T = 10, so .. K = 200
Now, R is 10, so T = 200/10 = 20...

OR

Directly.
S = kRT
k = 1/5
now R is changed so T = 20

Like? Yes (1) | No   

nidhi   9 years AGO

T is inversely proportional to R.
Therefore, T= k/10, 10=k/20, k=200. now, T=k/10=200/10=20

Like? Yes (1) | No   

Rajyalakshmi   9 years AGO

as T inversely varies then it becomes twice of R

Like? Yes (1) | No   

abhishek   9 years AGO

calculate the constant from the equation
T=K/R
put T=10,R=20

then K=200
the equation becomes T=200/R
put R=10

T=20

Like? Yes (1) | No   

meghana   9 years AGO

T varies inversely as R varies
so RT=constant
RT=R'T'
20*10=10*T'
T=20

Like? Yes (1) | No   

vikash kumar das   9 years AGO

as R=kT,where k is constant,putiing R=20 and T=10,we calculate the value of k.
Now putting R=10 n k=200 in T=k/R,we get T=20.

Like? Yes (1) | No   

akshay jain   9 years AGO

T is inversely proportional,if R is havled than T get doubled

Like? Yes (1) | No   

Gunjan Sharma   9 years AGO

As per question,
S=@R.....(1)
T=&/R....(2)

when R=20, S=40 and T=10 then @=2 and &=200.
When R changed to 10, then T=200/10=20 (Ans).

Like? Yes (1) | No   

sudiptaa   9 years AGO

S=pR
p= S/R = 40/20=2
T=q/R
q=TR=20*10=200
. ' . R=10 ; T= q/R= 200/10 = 20

Like? Yes (1) | No   

Aritra Chakraborty   9 years AGO

R inversely related to T. RT=k, say. R=20, T=10 => RT=200 i.e. when R=10, T=200/10=20.

Like? Yes (1) | No   

nirmal das   9 years AGO

as R varies inverse as T... then T=k/R..when R=20 and T=10 then k=200...if r is changed to 10 then T will be 20...

Like? Yes (1) | No   

Alok Singh   9 years AGO

If S is proportional to R
then according to the question S = K1*R then K1=2 So S=40
and as R=k2/T
then if K2=200 then T=10
so there will bw the value of T will be 20 when R=10

Like? Yes (1) | No   

Karthik   9 years AGO

R decreased by 10 which is half down
so T increases by half

Like? Yes (1) | No   

JITIN   9 years AGO

R is directly proportional to S and T is inversely proportional to R
i.e.., if R is increased or decreased ,S wud also be inc or dec in same ratio
here
R is divided by 2 so S will also divided by 2 but T will be multiplied by 2 cuz both T & R are inversely prop.
so,
S=20
R=10(given)
T=20

Like? Yes (1) | No   

Soma Naresh   9 years AGO

given T is inversely proportional to R
T=m/R
TR=m
given T=10, R=20
m=TR=10*20=200
If R=10
then T=m/R
T= 200/10=20

Like? Yes (1) | No   

kondapuram tirumalreddy   9 years AGO

Since R and T are inverse proportional
R is reduced to half
so T shoulde be icreased by double

Like? Yes (1) | No   

sarang pandey   9 years AGO

r changes from 20 to 10,-- s changes from 40 to 30,--t changes inversely with respect to r so r decreased by 10 t will increase by 10 so answer will be 20

Like? Yes (1) | No   

akanchha pandey   9 years AGO

bcz r=r/2=10
if t is inverse to r then
t=20

Like? Yes (1) | No   

marline   9 years AGO

T and R are inversely proportional. If R= 20 when T=10 then T must be 20 when R=10

Like? Yes (1) | No   

Sourabh Prasad   9 years AGO

ST/R is constant.

so 40*10/20 = 20*T/20
T= 20

Like? Yes (1) | No   

Gaurav Pratap Singh   9 years AGO

T is inversly propitional to R.
T became half so R became double.
Answer - R became 20

Like? Yes (3) | No (3)  

payal   9 years AGO

since r and t s inversely proportional to each other
if r=20 then t=10
if r=10 then t=20

Like? Yes (3) | No (3)  

TAUSEEF AMEEN   9 years AGO

As T is inversely proportional to r.
let K be proportionality constant.
then...
T=k/R
Putting R=20 and T=10
K=200......1)
now again T=K/R
putting k=200 and R =10
T=20
hence option 1 is correct ans

Like? Yes (4) | No (4)  

velmala gangadhar   9 years AGO

S=kR and T=c/R...we have R=20,T=10
Then constant c=200...
if R is changed to 10..so..T will be 20.........

Like? Yes (2) | No (2)  

Mousuma Roy   9 years AGO

40=k*20,k=2,10=(a/10),a=200,r=10,10=(200/t),t=20

Like? Yes (1) | No (1)  

MANUPOTI ANAND   9 years AGO

R1T1=R2T2
S0,T2=(R1T1/R2)
=(10*20)/10
=20

Like? Yes (3) | No (3)  

venkatesh   9 years AGO

T is inversely proposonal to R
T1*R1=T2*R2
T2=10*20/10
T2 =20

Like? Yes (1) | No (1)  

Gaurav Verma   9 years AGO

T inversly proportional to R
=> T=K/R .......(1)
taking, T=10,R=20, we get k=200
Now, putting values of k and R in (1). we get,
T=20

Like? Yes (1) | No (1)  

Kunal nemu   9 years AGO

S/TR is constant.
So, 40/20*10 = 40/10*T
T = 20

Like? Yes (1) | No (1)  

shilpa prakash   9 years AGO

S DIRECTLY R TINVERSLY 1/R
SO T=10 THEN R=20 WHEN R=10 T=20

Like? Yes (2) | No (2)  

Ramesh Sriram   9 years AGO

T1R1=T2R2
10*20=10*t2
t2=20

Like? Yes (1) | No (1)  

shivam dubey   9 years AGO

T inversely proportional to R

so r is become 10 then T become 20

ans

Like? Yes (1) | No (1)  

k sureshbabu   9 years AGO

R REDUCES TO 10
T GAINS 10

Like? Yes (1) | No (1)  

Amit chaturvedi   9 years AGO

According to question,
S ∝R and 1/T ∝R,
But S and R relationship is given just for creating confusion,
so so focus on T and R
If value of R is halved then value of T will be doubled
i.e 20

Like? Yes (3) | No (3)  

s.h.h.praveen   9 years AGO

s=kr and tr=p,where k and p are constants .
1)substitute the above values to know the constant values.
2)after that change the value of r to 10.we get the values of s=20 and t=20

Like? Yes (1) | No (1)  

Pesari Udayasree   9 years AGO

given that (s/t) proportional to r
according to the given values proportionate can be replaced as r=5(s/t)
now r=10, s=40, by substituting this we get t=20

Like? Yes (1) | No (1)  

Sandeep Kumar   9 years AGO

As given
S ~ R
So
S = k R ( k constant )
Also T ~ 1/ R ( inversely)
T = k/ R
Initially T = 10 R = 20
10 = k / 20 ; k = 200
Now
R = 10
T = 200/10; T = 20

Like? Yes (1) | No (1)  

Rahul Jadhav   9 years AGO

40=20=1/10
20=10=1/20

Like? Yes (1) | No (1)  

Rohit Agrawal   9 years AGO

S=k*R
T=m/R
R=20, S=20, T=10
=>m=200, k=2
at R=10
T=m/R= 200/10= 20

Like? Yes (1) | No (1)  

sanchit soni   9 years AGO

r halves and t doubles value

Like? Yes (1) | No (1)  

momin ashraf ahamed   9 years AGO

r1t1=r2t2 substitute r1=20,t1=10,r2=10

Like? Yes (1) | No (1)  

R.Shyaam Sunder   9 years AGO

since T is inversely proportional R,when R is decreased by 10 is increased by 10.Therefore T=10+10=20
T=20.

Like? Yes (2) | No (2)  

SK INTAJ MOHAMMAD   9 years AGO

S=K1*R and T=K2*1/R
K1=2 and K2=200
T=200/10=20

Like? Yes (1) | No (1)  

DEVENDRA PAL SINGH RATHORE   9 years AGO

R AND T ARE inversely SO

Like? Yes (2) | No (2)  

minakshi kumari   9 years AGO

s=2r
t=200/r

Like? Yes (1) | No (1)  

Vikas Jha   9 years AGO

rule of proportinality

Like? Yes (1) | No (1)  

santhosh   9 years AGO

s=xt
t=x/r

Like? Yes (1) | No (1)  

siddhi datri   9 years AGO

s=2r
t=200/r
=>t=200/10=20

Like? Yes (1) | No (1)  

Nilesh Kumar   9 years AGO

as t changes inversely of r

Like? Yes (1) | No (1)  

Niladrit Mondal   9 years AGO

since s varies directly with r
den s=kr
40=20k
k=2
now r inversely varies with t
r=k/t
20=k/10
therefore,k=200
now ,r=10
therefore t=k/r,t=200/10=20

Like? Yes (1) | No (1)  

baby posamma   9 years AGO

(s1/s2)=(r1/r2)=(t2/t1)=> (40/s2)=(20/10)=(t2/10)=> t2=20

Like? Yes (1) | No (1)  

himani kukreti   9 years AGO

T is inversely proportional to r , if r value will Dec then t value will Inc up

Like? Yes (1) | No (1)  

G MAHESH   9 years AGO

find constants k1 and k2,using given data ..and after that substitue new values to get answer

Like? Yes (1) | No (1)  

MUNISH YADAV   9 years AGO

s=k1r, tr=k2 Putting values we get k1,k2=2,200. Again put r=10,k2=200 in second equation to get t.

Like? Yes (1) | No (1)  

Kshitiz Khandelwal   9 years AGO

T varies inversely as R
Then
R is reduced by half, so T will be increased by factor of 2
so T will be 20

Like? Yes (1) | No (1)  

Subhendu Pradhan   9 years AGO

s=k1r,t=k2/r;
so, k2=t*r;
t must be 2 times of its value keeping constant the value of k2 while changing the value of r by half times

Like? Yes (1) | No (1)  

Rupkatha Banerjee   9 years AGO

As T varies inversely as R varies, T=K/R where K is a constant.
If R=20 & T=10 K=200
If R=10, T=K/R=200/10=20

Like? Yes (1) | No (1)  

Pillalamari Bala Sri Jyothi   9 years AGO

AS R DECREASED BY 10 , T VALUE INCREASED BY 10 MEANS 20

Like? Yes (1) | No (1)  

swasthika   9 years AGO

R=K/T (K is the constant of proportionality)

Like? Yes (1) | No (1)  

Deepanshu Chaturvedi   9 years AGO

let R=x/T so,from question 20=x/10 =>x=200
when R=10 value of T=x/R=200/10=20.

Like? Yes (1) | No (1)  

Anik Chaudhuri   9 years AGO

T1/T2=R2/R1

Like? Yes (1) | No (1)  

Abhisek Ghosh   9 years AGO

t varies inversely with r,if r is reduced to half,then t will be multiplied by 2

Like? Yes (1) | No (1)  

YASWANTH REDDY   9 years AGO

As R is inversely proportional to T, RT = constant.
new T value = 20*10/10 = 20

Like? Yes (1) | No (1)  

Deepali Tyagi   9 years AGO

R n T are inversely proportional i.e why for R= 10 .....T=20

Like? Yes (1) | No (1)  

MADHUBABU   9 years AGO

As T is inversely proportional to R
=> T1R1=T2R2
=> T2=(T1*R1)/R2
=> T2=(20*10)/10
=> T2=20

Like? Yes (2) | No (2)  

Paul Rohit   9 years AGO

S = x*R , T = y/R given that when R = 20, T = 10 so y = 200. Therefore when R = 10 then T = 200/10 = 10.

Like? Yes (1) | No (1)  

gourav   9 years AGO

t inversely proportional to r => r*t=constant. and when t=10 and r=20 then constant =200 and when r changed to 10 so t will be 200/10=20

Like? Yes (1) | No (1)  

Anurag Raj   9 years AGO

because T is inversely proportional

Like? Yes (1) | No (1)  

Parthasarathi.S   9 years AGO

T=c/R
10=c/20
20=c/10
=>T=20

Like? Yes (1) | No (1)  

RUPANJAN ROY   9 years AGO

as T varies inversely with r therefore TR=const,
T1R1=T2R2
10*20=10*T2

Like? Yes (1) | No (1)  

SOURABH   9 years AGO

s=x*r
x=40/20=2
r=k/t
k=20*10=200
10=200/t
t=20

Like? Yes (2) | No (2)  

Arpan Ganguly   9 years AGO

let s =kr and t=l/r where k and l are constant
if r= 20 and s=40 then easily we get k=2
and t = l/20 , and t is 10 so here l=20*t=20*10=200
r has changed to 10 so t will be
t=200/10 = 20 so option 1 is correct

Like? Yes (1) | No (1)  

Divakar   9 years AGO

R changed 20 to 10. It decreases by half(R/2). The condition is T varies as R varies.So T increases by double(10*2=20).

Like? Yes (1) | No (1)  

Vinit Patil   9 years AGO

T is inveresly proportional to R

Like? Yes (1) | No (1)  

praveendas   9 years AGO

the given condition is
s->r->1/t.
40->20->1/10.
if r is changed to 10 then s changes to 20,as it is directly proportional to r .t changes to20 as it is inversely proportional to r.
20->10->1/20.
option 1

Like? Yes (2) | No (3)  

aman aditya   9 years AGO

t=20

Like? Yes (1) | No (2)  

DURGESH KUMAR   9 years AGO

for t is inversely .. proportion constant is 200... then put value

Like? Yes (1) | No (2)  

shikha   9 years AGO

S=kr
T=k/r
10=k/20
20=k/10

Like? Yes (2) | No (3)  

shilpa singh   9 years AGO

S=kr
T=k/r
10=k/20
20=k/10

Like? Yes (2) | No (3)  

ankit chavhan   9 years AGO

K & p are constant
S=k * r
T=p/r
Given : r =20,s =40,t =10
Since , value of constant will always remain the same...
So, on solving we get

P= 200 and k= 2
Now r=10 and p=200

Therefore t= 20

Like? Yes (1) | No (2)  

Sudharsan   9 years AGO

s=4 times T

t = 200* (1/R)

Like? Yes (1) | No (2)  

aishi sur   9 years AGO

For R inversely proportional to T , 20 =k/10 so k=200

Next case R=10 so T = k/R =20

Like? Yes (1) | No (2)  

REVATHIVENKATESAN   9 years AGO

ST/R is constant.

so 40*10/20 = 20*T/20
T= 20

Like? Yes (1) | No (2)  

SHAIK MAHABOOB BASHA   9 years AGO

T varies inversely as R varies
so if R=20 then T is 10
R*T=1
20*10=200
If R=10 T=?
10*T=200
T=20

Like? Yes (2) | No (3)  

Ajay Kumar Gupta   9 years AGO

ST/R=Constant
so 40*10/20=20*T/20
T=20

Like? Yes (1) | No (2)  

BIRANCHI NARAYAN RATH   9 years AGO

s=c1*R
t=c2/R

solving k=2

solving in that way t=20

Like? Yes (1) | No (2)  

shubham singh   9 years AGO

T=k/R
i.e. TR=constant
therefore T=20

Like? Yes (1) | No (2)  

jyoti   9 years AGO

tvaries inversly ti r

Like? Yes (2) | No (3)  

ADARSH GAURAV   9 years AGO

20 is the answer

Like? Yes (1) | No (2)  

sukriti singh   9 years AGO

s proportional to r
=> s=xr, x is some constant.
=>t=y/r, r is some proporionality constant.
now at some point when, r=20 s=40 and t=10.
40=x*20
=> x=2.
similarily,
t=y/r
=> 10=y/20
=>y=200.
so when r=10
=>t=200/10=20. ans.

Like? Yes (1) | No (3)  

Abhinav Akash   9 years AGO

At present:R=20,S=40 , T=10 S directly proportional to R ,So Let K be the proportionality constant,So S=KR
K=2
T is inversely proportional to R so
T=C/R ( C be proportionality constant Say)
So C=200
Now when R is changed to 10,then T=200/10
i.e equal to 20

Like? Yes (1) | No (3)  

SHAHARBAN O   9 years AGO

T varies inversely as R varies. Here R reduced by 10 the inversely T will be increased by 10.

Like? Yes (1) | No (3)  

deepthi pusala   9 years AGO

since t varies inversely with r.r is decreased by 10 so,t should be increased by 10.

Like? Yes (1) | No (3)  

Pratiksha Gupta   9 years AGO

t inversely varies as R. So if we decrease the value of R then value of t will increase

Like? Yes (1) | No (3)  

14 Sep 2015 Solve

(1 / 1+a^(n-m)) + (1 / 1+a^(m-n)) is equal to

OPtion

1) 0
2) 1
3) 1/2
4) a^(m+n)
5) a^(m-n)
6) 1/a^(m+n)
7) 1/a^(m-n)
8) 1/a^(n-m)
9) a^(n-m)
10)None of these

Solution

Solve
a^m + a^n / a^m + a^n = 1

Option 2)

Correct Option: 2 Best Solution (135)

MOHAN   9 years AGO

GIVEN [1 / 1+a^(n-m)] + [1 / 1+a^(m-n)]

=[1/1+(a^n/a^m)]+[1/1+(a^m/a^n)]

=[1/(a^m+a^n/a^m)]+[1/(a^n+a^m/a^n)]

=[a^m/(a^m+a^n)]+[a^n/(a^n+a^m)]

=[a^m+a^n]/[a^m+a^n]

=1
so answer is 2

Like? Yes (30) | No (15)  

manideep   9 years AGO

->we know that a^(m-n)=a^m/a^n
->By using the above formula the problem can be solved easily
->(1/1+(a^n/a^m))+(1/1+(a^m/a^n))
->Take LCM of denominators of each terms individually
->(1/((a^m+a^n)/a^m))+(1/((a^n+a^m)/a^n))
->(a^m/(a^m+a^n))+(a^n/(a^n+a^m))
->By taking LCM, both numerator and denominator gets cancelled by 1.
->The answer is 1

Like? Yes (17) | No (4)  

Amit chaturvedi   9 years AGO

suppose a=1,m=2,n=3
put these values in equation
solving it
(1 / 1+1^(3-2)) + (1 / 1+1^(2-3))

1

Like? Yes (4) | No   

anjana sethi   9 years AGO

1/1+a^n-m +1/1+a^m-n = a^n +a^m/a^n+a^m = 1

Like? Yes (5) | No (1)  

J E Tejeswar Gowd   9 years AGO

1/(1+a^(m-n))+(a^(m-n))/(1+a^(m-n))=1

Like? Yes (5) | No (2)  

suraj kumar   9 years AGO

a^m+ a^n ÷a^m+a^n=1

Like? Yes (4) | No (1)  

ramya   9 years AGO

Take the first term:
1/1+a^(n-m) => 1/1+a^-(m-n)
=> a^(m-n) /1+a^(m-n) is the first term
Add it with second term you get :

1+a^(m-n) / 1+a^(m-n) => 1
So option 2

Like? Yes (3) | No   

Animesh Gupta   9 years AGO

for any value of n and m. the condition satisfies a^n+1/a^n+1.
which equals to 1.

Like? Yes (3) | No   

MURUGAVEL   9 years AGO

1/1+a^(n-m) = a^m/a^m+a^n
similarly
1/1+a^(m-n) = a^n/a^m+a^n
substituting in question we get ans 1,(i.e) option 2

Like? Yes (6) | No (3)  

praveendas   9 years AGO

the given expression can be rewritten like (a^m/a^m+a^n)+(a^n/a^m+a^n).
take lcm then numerator and denominator gets cancelled.that's it
option 2

Like? Yes (3) | No (1)  

kriti kankariya   9 years AGO

1/(1+((a^n)/(a^m))) = a^m/(a^m + a^n)
1/(1+((a^m)/(a^n))) = a^n/(a^m + a^n)
adding we will get 1

Like? Yes (4) | No (2)  

sudiptaa   9 years AGO

(1+a^m-n +1+a^n-m)/(1+a^m-n)(1+a^n-m))=2

Like? Yes (2) | No   

SUMIT PAREEK   9 years AGO

(1 / 1+a^(n-m)) + (1 / 1+a^(m-n)) =(1+a^(n-m)+1+a^(m-n))/((1+a^(n-m))*(1+a^(m-n)))
=(2+a^(m-n)+a^(n-m))/(2+a^(m-n)+a^(n-m))
=1

Like? Yes (4) | No (2)  

Rohit Agrawal   9 years AGO

affter addition the numerator and denominator pairs will cancel out

Like? Yes (2) | No   

shivam dubey   9 years AGO

2+ a^(m-n)+a^(n-m) / 2+a^(m-n)+a^(n-m) = 1 ans

Like? Yes (2) | No   

SANJIT PRASAD   9 years AGO

assume n-m=x;
1+a^x/1+a^x=1

Like? Yes (3) | No (1)  

Moumita Choudhury   9 years AGO

1/ (1+k) + 1 / (1+1/k) =1

Like? Yes (3) | No (1)  

Arvind kumar   9 years AGO

(1 / 1+a^(n-m)) + (1 / 1+a^(m-n))
=(1 / 1+a^(n-m))+(1/1+(1/a^(n-m)))
=(1 / 1+a^(n-m))+(a^(n-m)/(1+a^(n-m)))
=(1 / 1+a^(n-m))/(1 / 1+a^(n-m))
=1

Like? Yes (2) | No   

himanshu shekhar   9 years AGO

(1/(1+a^n-m)+(1/(1+a^m-n)
=let n-m=x
ymthen (1/a^x)+(1/a^-x)
=1

Like? Yes (2) | No   

Deepali Tyagi   9 years AGO

This is of the form x / (x+1)+1/(x+1) where x=a^(m-n)
Option 2 is correct

Like? Yes (2) | No   

Ajay Kumar Gupta   9 years AGO

(1/(1+a^m/a^n))+(1/(1+a^n/a^m))
=a^m/(a^m+a^n)+a^n/(a^m+a^n)
=(a^m+a^n)/(a^m+a^n)
=1.

Like? Yes (2) | No   

Kaviya   9 years AGO

answer is 1
(1 / 1+a^(n-m)) + (1 / 1+a^(m-n))
by taking lcm :
1+a^(m-n)+1+a^(n-m)
=-------------------------------------
(1+a^(m-n))*(1+a^(n-m))

here a^(m-n) = a^-(n-m)= 1/ a^(n-m)
apply this in above equation
2+ a^(n-m)+ (1/a^(n-m))
=-----------------------------------------
(1+a^(n-m))*(1+ (1/a^(n-m)))

2a^(n-m)+1+ [ a^(n-m)*a^(n-m)]
=-----------------------------------------------
[ 1+a^(n-m)]^2

2a^(n-m)+1+ a^2(n-m)
=-----------------------------------------------
[ 1+a^(n-m)]^2

The numerator is of the form a^2 +b^2 +2ab = (a+b)^2
2a^(n-m)+1+ a^2(n-m) = [ 1+a^(n-m)]^2

[ 1+a^(n-m)]^2
=------------------------------------
[ 1+a^(n-m)]^2
=1

Like? Yes (2) | No   

bhaskar   9 years AGO

(1 / 1+a^(m-n))=a^(n-m)/1+a^(n-m)

Like? Yes (2) | No (1)  

SAGNIK DATTA   9 years AGO

case 1 : take n=2,m=1, a=2
case 2 : take n=3, m=1, a=2
both cases answer is 1

Like? Yes (2) | No (1)  

PRAGATHI G   9 years AGO

first term results as a^m/(a^m+a^n). second term results as a^n/(a^n+a^m). so addition of both terms results as 1

Like? Yes (3) | No (2)  

TAUSEEF AMEEN   9 years AGO

take lcm of (1+a^(n-m)) and (1+a^(m-n))..
will be same as numerator in addition..
hence 1.

Like? Yes (2) | No (1)  

RAVAL   9 years AGO

assume m=4,n=3,a=2

Like? Yes (2) | No (1)  

alpesh kurhade   9 years AGO

By solving simply we get ans: 1

Like? Yes (2) | No (1)  

Abhinav Akash   9 years AGO

Simple Fractional sum .

Like? Yes (2) | No (1)  

Danda Sindhura   9 years AGO

LET m,n be 1,2
by substituting in the given problem
we get numerator and denominator same ...
so ans is 1

Like? Yes (1) | No   

shikha   9 years AGO

1 / 1+a^(n-m)) + (1 / 1+a^(m-n))
=1+a^(m-n)+1+a^(n-m)/2+a^(m-n)+a^(n-m)
=1

Like? Yes (1) | No   

Sruthi Sreejan   9 years AGO

(1 / 1+a^(n-m)) + (1 / 1+a^(m-n))

= (1 / 1+a^ -(m-n)) + (1 / 1+a^(m-n))
=(a^(m-n) /1+a^(m-n)) + (1 / 1+a^(m-n))
=(1+a^(m-n) / 1+a^(m-n))
=1

Like? Yes (1) | No   

shilpa singh   9 years AGO

1/1+a^n-m+1/1+a^m-n=1

Like? Yes (1) | No   

Gaurav Pratap Singh   9 years AGO

given question is (1/(1+a^n-m))+(1/(1+a^m-n))
we can write it as (1/(1+a^n-m))+(1/(1+ a^ (n-m)^ -1 ) )
=(1+a^n-m)/(1+a^n-m)
=1

Like? Yes (1) | No   

Arnab Maity   9 years AGO

= (1 / 1+a^(n-m)) + (1 / 1+a^(m-n))
= (1 / 1+a^-b) + (1 / 1+a^b) [let m-n = b therefore -(m-n)= -b]
= (1 / 1+(1/a^b)) + (1 / 1+a^b)
= (a^b/1+a^b) + (1 / 1+a^b)
= (1 + a^b)/(1 + a^b)
= 1

Like? Yes (1) | No   

K.THARUN KUMAR   9 years AGO

(a^(m+n)/a^(m+n)+1)+(1/a^(m+n)+1)=1

Like? Yes (1) | No   

SK INTAJ MOHAMMAD   9 years AGO

a^m/(a^m+a^n)+a^n/(a^n+a^m)=1;

Like? Yes (1) | No   

Ranjana Gautam   9 years AGO

1/1+a^(n-m)+1/1+a^(m-n)
=a^(m-n)/1+a^(m-n)+1/1+a^(m-n)
=1

Like? Yes (1) | No   

sumitha saseendran   9 years AGO

a^n-m = a^n / a^m
similarly a^m-n = a^n / a^m
cross multiplying the two terms in the question and cancelling out common terms in numerator and denominator of the resulting fraction will finally give 1, i.e option 2

Like? Yes (1) | No   

meghna jain   9 years AGO

we wil write a^n/a^m and vice versa in other part and wil take the lcm . it will give 1 as ans

Like? Yes (1) | No   

k. asha   9 years AGO

a^m/(a^m+a^n)+a^n/(a^n+a^m)=1

Like? Yes (1) | No   

Deepak   9 years AGO

Let x = n-m,

1/ (1+a^x) + 1/(1+a^-x) = 1/(1+a^x) + a^x / (1+ a^x) = 1

Like? Yes (1) | No   

Praveenkumar Kalikeri   9 years AGO

Let m-n =p
then
1/( 1 +a^-p) + 1 / (1+a^p)
??
a^p /(1 +a^p) + 1/( 1 +a^p)
??
(1 +a^p)/(1+a^p)
?? =1
Hence option( 2 ). 1

Like? Yes (1) | No   

Rupkatha Banerjee   9 years AGO

given expression = (a^m/(a^m+a^n)) + (a^n/(a^m+a^n))
= (a^m+a^n)/(a^m+a^n)
=1

Like? Yes (1) | No   

Pradeep   9 years AGO

numerator and denominator will be cancelled

Like? Yes (1) | No   

Ankita Sharma   9 years AGO

m=0,n=0

Like? Yes (1) | No   

Ramesh Sriram   9 years AGO

by taking LCM and simplification

Like? Yes (1) | No   

UJJWAL KAMAR   9 years AGO

a^m/(a^m+a^n) + a^n/(a^m+a^n)

= (a^m+a^n)/(a^m+a^n)

=1

Like? Yes (1) | No   

Kanchan Patil   9 years AGO

(1/(1+(a^n/a^m)))+(1/(1+(a^m/a^n)))=
(a^m/(a^m+a^n))+(a^n/(a^n+a^m))=
(a^m+a^n)/(a^m+a^n)=1

Like? Yes (1) | No   

jyoti   9 years AGO

solving first of addends by reciprocating the "a" term, we get:
(1 / 1+(1/a^(m-n))

Simplifying it further we get:
(a^(m-n) / 1 + a^(m-n))

now considering the whole addition, that is:
(a^(m-n) / 1 + a^(m-n)) + (1 / 1+a^(m-n))

we get:
(a^(m-n) + 1 ) / ( 1 + a^(m-n))
which eventually results in 1.

So correct option is (2)

Like? Yes (1) | No   

sanchit soni   9 years AGO

1/1+a^n-m + 1/1+a^m-n =
1+a^m-n + 1+a^n-m/1+a^m-n + 1+a^n-m = 1 ans

Like? Yes (1) | No   

Devendra Marghade   9 years AGO

[1/(1+a^(n-m))] + [1/(1+a^(m-n))]
As (n-m)=-(m-n)
So [1/(1+a^-(m-n))]+[1/(1+a^(m-n))]
If a^(m-n)=x ,then
[1/(1+x^-1)] +[1/(1+x)]
=1/(1+(1/x)) + 1/(1+x)
=x/(1+x) + 1/(1+x)
=(1+x)/(1+x)
=1
Option 2)

Like? Yes (1) | No   

MUNISH YADAV   9 years AGO

For n=m=0,1 values of expression is 1 for all a.

Like? Yes (1) | No   

Akash Kumar   9 years AGO

(1 / 1+a^(n-m)) + (1 / 1+a^(m-n))
adding both terms
=(1+a^(n-m)+1+a^(m-n))/((1+a^(n-m))*(1+a^(n-m)))
(solving numerator and denominator we get the following
=(2+a^(n-m)+a^(m-n))/(2+a^(n-m)+a^(m-n))
=1

Like? Yes (1) | No   

Dhrubo   9 years AGO

== [ 1 / {1 a^ n / a^ m} ] [ 1 / {1 a^ m / a^ n} ]
== [{a^ m / (a^m a ^ n)} {a^ n / (a^m a ^ n)} ]
== (a^ m a ^ n) / (a^ m a ^ n)

== 1 answer

Like? Yes (1) | No   

Bhavya Manasa   9 years AGO

(1/1+a^(n-m))+(1/1+a^(-(n-m))
(1/1+a^(n-m))+(1/(1+1/a^(n-m)))
(1/1+a^(n-m))+(a^(n-m)/1+a^(n-m))
(1+a^(n-m))/(1+a^(n-m))
1

Like? Yes (1) | No   

Arpan Ganguly   9 years AGO

1+a^(n-m) = 1+(a^n/a^m) = (a^m+a^n)/a^m and
1+a^(m-n) = 1+(a^m/a^n) = (a^m+a^n)/a^n
so
(1 / 1+a^(n-m)) + (1 / 1+a^(m-n))=
(a^m/(a^m/a^n))+(a^n/(a^m/a^n))= ((a^m+a^n)/(a^m+a^n))=1

Like? Yes (1) | No   

shivam gaba   9 years AGO

1/1+an/am+1/1+am/an=1

Like? Yes (1) | No   

abhishek   9 years AGO

just simplify it...

firt take LCM
then you get denominator same as that of numerator
so equals 1

Like? Yes (1) | No   

pratik raj   9 years AGO

a^n-m will get cancelled if we take - common from second term

Like? Yes (1) | No   

Sriparna Boote   9 years AGO

Lets assume m=1 and n=2
Then
1/(1+a^-1)+1/(1+a)=1/(1+(1/a))+1/(1+a)=a/(1+a)+1(/(1+a)=(a+1)/(1+a)=1

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Debashish Mishra   9 years AGO

(1 / 1+a^(n-m)) + (1 / 1+a^(m-n))
=(1 / 1+a^(n-m)) + (1 / 1+a^-1(n-m))
=(1 / 1+a^(n-m)) + (a^(n-m)/ 1+a^(n-m))
=(1+a^(n-m))/(1+a^(n-m))
=1

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avinash choori   9 years AGO

take a=4 m=2 and n=3
1/1+4^3-2 + 1/1+4^2-3=1

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prashant   9 years AGO

after solving the equation we get :
(2+a^(m-n)+a^(n-m))/(2+a^(m-n)+a^(n-m))=1

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Umesh sahu   9 years AGO

because they are cancelled all together when give any value assume in m and n

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YASWANTH REDDY   9 years AGO

if we simplify the given expression, we finally get same value in numerator and denominator and therefore the answer is 1

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adarsh   9 years AGO

on solving the above we get 1

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meghana   9 years AGO

a^(n-m) =p and a^(m-n) = 1/p

(1/(1+P))+(P/(P+1)) = (p+1)/(p+1) =1

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baby posamma   9 years AGO

(1/1+a^(n-m))+(a^(n-m)/(1+a^(n-m))=1

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sushil singh   9 years AGO

addition by taking lcm

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Akhila   9 years AGO

1/1+a*(n-m)+1/1+1/a*(n-m)

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keerthi choudhry   9 years AGO

1 / 1+a^(n-m) + 1 /1+a^(m-n) = 1/(1+a^n/a^m) + 1/(1+a^m/a^n)
= a^m/ a^m+a^n + a^n/ a^n+a^m
= a^n+a^m / a^n+a^m
=1(option 2)

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mithilesh kumar   9 years AGO

given (1 / 1+a^(n-m)) + (1 / 1+a^(m-n))
=>a^m/a^n+a^m +a^n/a^m+a^n
=>1

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payal   9 years AGO

on solving it looks like (2+a^m-n+a^n-m)/(2+a^m-n+a^n-m)=1

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Diksha tiwari   9 years AGO

1/(1+a^(n-m))+ 1/(1+a^(m-n)) =1/(1+a^(n-m))+a^(n-m)/(1+a^(n-m))
=(1+a^(n-m))/(1+a^(n-m))=1

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Maneesh Shringi   9 years AGO

(1/1+a^n-m) + (1/1+a^m-n)= 1/1+(a^n/a^m)+1/1+(a^m/a^n)
=a^m/(a^m+a^n) + a^n/(a^n+a^m)
=a^m+a^n/a^m+a^n
=1

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Anand Kumar Mehta   9 years AGO

After adding
Numerator becomes
(1+a^(m-n)+1+a^(n-m))
And denominator becomes same 1+a^(m-n)+a^(n-m)+a(n-m+m-n) which is equal to numarator ......so ans.is 1 option 2 is correct

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Subhendu Pradhan   9 years AGO

(1/1+a^n/a^m)+(1/1+a^m/a^n)
=a^m/(a^m+a^n)+a^n/(a^m+a^n)
=a^m+a^n/a^m+a^n
=1

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s.h.h.praveen   9 years AGO

just by simplification and a formula (a^n-m=a^n/a^m)

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kondapuram tirumalreddy   9 years AGO

by solving we get
2+a^n-m+a^m-n/2+a^m-n+a^n-m
=1

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Aman Gaurav   9 years AGO

If base are same divide power should be subtracted
so,
1/1+(a^n/a^m) + 1/1+(a^m/a^n)
so,
a^m/a^m+a^n + a^n/a^m+a^n
so,
a^m+a^n/a^m+a^n
so
1

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Aman   9 years AGO

If base are same divide power should be subtracted
so,
1/1+(a^n/a^m) + 1/1+(a^m/a^n)
so,
a^m/a^m+a^n + a^n/a^m+a^n
so,
a^m+a^n/a^m+a^n
so
1

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lakshmi priya   9 years AGO

on taking lcm & canceling

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S.RAJASHREE   9 years AGO

PUTa=3,n=6,m=5,solving we get 1

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Vikas Jha   9 years AGO

Solving it gets to 1

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akhil   9 years AGO

change a^(n-m)as 11/a^(m-n) and take l.c.m

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Pesari Udayasree   9 years AGO

let n-m=b; then m-n=-b
by substituting this values we get the equation as
(1/1+a^b)+(1/1+a^-b)
since a^-b=1/a^b
then we get (1+a^b)/(1+a^b)=1

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Nick Jain   9 years AGO

(2+a^(n-m)+a^(m-n))/(2+a^(n-m)+a^(m-n))=1

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Mayank   9 years AGO

(1/1+a^2)+(1/1+a^-2)
=(1/1+a^2)/(1/1+a^2)
=1

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mounika   9 years AGO

(1/1+a^2)+(1/1+a^-2)
=(1/1+a^2)/(1/1+a^2)
=1

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jagdish jakhar   9 years AGO

[1+a^(m-n)+1+a^(n-m)]/2+a^(m-n)+a^(n-m)=1

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Anand Kumar Sharma   9 years AGO

(1 / 1+a^(n-m)) + (1 / 1+a^(m-n))
=(1/1+a^(n-m))+(a^(n-m)/1+a^(n-m))
=(1+a^(n-m))/(1+a^(n-m))
=1

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krishna prasad   9 years AGO

after simplification numerator and denominator are equal

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Anubrindha   9 years AGO

Use simple cross multiplication we can get 1 as final answer

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Surabhi Yadav   9 years AGO

by solving it (1/1+a^n-m)+(1/1+a^m-n)
=(1/1+(a^n/a^m))+(1/1+(a^m/a^n)
=(a^m/(a^m+a^n))+(a^n/(a^m+a^n))
=1

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K.Anitha   9 years AGO

When simplified equation becomes as
(2+a^(m-n)+a^(n-m))/(1+a^(m-n)+a^(n-m)+a^0)=1

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prashant trivedi   9 years AGO

simple just solve

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surya   9 years AGO

both numerator and denominator are same after solving

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rahul shaw   9 years AGO

by solving the equations we get answer is 1
Just we have to take -ve sign common frpm 2nd term and simplify.

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Kunal nemu   9 years AGO

1 / 1+(a^n/a^m) + 1 / 1+(a^m/a^n)
=1 / ((a^n+a^m)/a^m) + 1 / ((a^n+a^m)/a^n)
=a^m/(a^n+a^m) + a^n/(a^n+a^m)
=(a^n+a^m) / (a^n+a^m)
=1

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john pranay   9 years AGO

a^m+a^n/a^m+a^n=1

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vimal tiwari   9 years AGO

1/1+a^m/a^n => a^n / a^n +a^m
and next term is solved as same., it becomes
a^m/a^n+a^m

on summing both we get =1

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Arvind   9 years AGO

(a^(m)/(a^(m)+a^(n)))+(a^(n)/(a^(m)+a^(n)))

Like? Yes (1) | No   

Mugesh sivagnanam Krishnapillai   9 years AGO

(1 / 1+a^(n-m)) + (1 / 1+a^(m-n))
=[2+a^(m-n)+a^(n-m)] / [1+a^(n-m))*(1+a^(m-n)]
=[2+a^(m-n)+a^(n-m)]/[2+a^(m-n)+a^(n-m)]
=1.

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velmala gangadhar   9 years AGO

(1/1+a^(n-m))+1/(1+1/a^n-m)..
(1/1+a^(n-m))+a^n-m/(1+a^n-m)..
it will become 1......

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MADHUBABU   9 years AGO

=>1/(1+(a^n/a^m))+1/(1+(a^m/a^n))
=>a^m/(a^m+a^n) +a^n/(a^n+a^m)
=>(a^m + a^n)/(a^m + a^n)
=> 1.

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jayaram   9 years AGO

a^m/(a^m+a^n)+a^n/(a^m+a^n)=1

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Priya Srimani   9 years AGO

= 1/{1+ (a^n+a^m)} + 1/1+(a^m+a^n)}
=1/{(a^m+a^n)/ a^m} + 1/{(a^n+a^m)/a^n}
= {a^m/(a^m+a^n)} + {a^n/(a^n+a^m)}
= (a^m+a^n)/(a^m+a^n)
= 1

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Sharath   9 years AGO

1/1+a^(n-m) + 1/1+a^-(n-m)
if we solve this we get
1/1+a^(n-m) + a^(n-m)/1+a^(n-m) = 1
so, option 2.

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saqib khan   9 years AGO

let n-m=x
then, m-n=-x
take LCM and on solving numerator and denominator will get cancelled and we will get 1.

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ramakrishna   9 years AGO

(a^m/(a^m+a^n))+(a^n/a^m+a^n))=
(a^m+a^n)/(a^m+a^n)=1

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CHANDAN KUMAR   9 years AGO

(a^m/a^m+a^n) +(a^n /a^n+a^m) =1

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Parthasarathi.S   9 years AGO

m-n=x
[1/(1+a^-x)]+ [1/(1+a^x)]
=[(a^x)/(1+a^x)] + [1/(1+a^x)]
=(1+a^x)/(1+a^x)
=1

Like? Yes (1) | No   

Saurabh Agrawal   9 years AGO

(1 / 1+a^(m-n)) = (n-m) / 1+a^(n-m)
(1 / 1+a^(n-m))+((n-m) / 1+a^(n-m)) = 1

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MANUPOTI ANAND   9 years AGO

(1 / 1+a^(n-m)) + (1 / 1+a^(m-n))=(1/(1+(1/a^m-n)))+ (1 / 1+a^(m-n))
=((a^m-n)/ (1 / 1+a^(m-n)))+ (1 / 1+a^(m-n))
= (1 / 1+a^(m-n))/ (1 / 1+a^(m-n))
=1

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RUPANJAN ROY   9 years AGO

1/(1+(a^n/a^m))+1/(1+(a^m/a^n))
this sums up to 1

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Gowsalaya G   9 years AGO

(1/(1+a^(n-m))+(1/1+a^(m-n))
=(1+a^(m-n)+1+a^(n-m))/((1+a^(n-m))(1+a^(m-n)))
=(2+a^(m-n)+a^(n-m))/(2+a^(m-n)+a^(n-m))
=1

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Animesh   9 years AGO

let m-n=x ,then 1/a^x + 1/a^-x =1

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Nandkishor jaiswal   9 years AGO

(1/1+a^(n-m))+(1/1+a^-(n-m))
=(1/1+a^(n-m)+(a^(n-m))/1+a^(n-m))
=1+a^(n-m)/1+a^(n-m)
=1

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sukriti singh   9 years AGO

1/(1+a^m-n)+1/(1+a^n-m)
=(1+a^m-n+1+a^m-n)/(1+a^m-n)*(1+a^-(m-n))
=(2+a^m-n+a^-(m-n))/(1+a^m-n)*(1+a^-(m-n))
=(2*a^m-n+1+a^2m-n)/a^m-n*(1+a^m-n)*(1+a^-(m-n))
=(a^2m-n+1)^2/(1+a^m-n)*(1+a^m-n)
=we will get 1 solving this..
so ans is option 2.

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rajat gupta   9 years AGO

a^m+a^n/a^m+a^n=1

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shafi   9 years AGO

no need of much explanation for this

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Ishita Chakraborty   9 years AGO

(1 / 1+a^(n-m)) + (1 / 1+a^(m-n))
=(1 / 1+a^(n-m)) + (1 / 1+a^ -(n-m))
=(1 / 1+a^(n-m)) + (1 / 1+(1/a^(n-m)))
=(1 / 1+a^(n-m))+ (a^(n-m)/1+a^(n-m))
=(1+a^(n-m))/(1+a^(n-m))

Like? Yes (1) | No   

Subhasri Pal   9 years AGO

(1 / 1+a^(n-m)) + (1 / 1+a^(m-n))
=(1 / 1+a^(n-m)) + (1 / 1+(1/a^(n-m)))
=a^(n-m)+1/a^(n-m)+1
=1

Like? Yes (1) | No   

kumar ajay   9 years AGO

1/(1+(a^n/a^m))+1/(1+(a^m/a^n))
a^m/(a^m+a^n)+a^n/(a^m+a^n)=1

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Shubham Raj   9 years AGO

the correct ans is 1
option 2)1

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Deepanshu Chaturvedi   9 years AGO

let n-m=y
so, from equation
(1/(1+a^y))+(1/(1+a^-y))
=> (1+a^y)/(1+a^y)=1

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Mayank Aditya   9 years AGO

(1 / 1+a^(n-m)) + (1 / 1+a^(m-n))
=(1 / 1+a^(n-m))+ (a^(n-m) / 1+a^(n-m))
=1

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Deepak Agarwal   9 years AGO

let n=1, m=2

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Kethineni Vinodh   9 years AGO

on expanding num/dem=1

Like? Yes (1) | No (1)  

SAI TEJA NALLA   9 years AGO

(1 / 1+a^(n-m)) + (1 / 1+a^(m-n))
(1 / 1+a^(n-m)) + (a^(n-m) / 1+a^(n-m))
1+a^(n-m)/1+a^(n-m)=>1

Like? Yes (1) | No (1)  

Nizamuddin S   9 years AGO

(a^(m+n)/a^(m+n)+1) + (1/a^(m+n)+1) =1

Like? Yes (1) | No (1)  

nirmal das   9 years AGO

1+a^(n-m)=(a^m+a^n)/a^m
in this way another part is solved....then if we add their reciprocal then we get 1..

Like? Yes (1) | No (1)  

pavani mongam   9 years AGO

(1+a^(m-n)+1+a^(n-m))/(1+a^(n-m))(1+a^(m-n))
=2+a^(m-n)+a^(n-m)/(2+a^(m-n)+a^(m-n))
=1

Like? Yes (1) | No (1)  

preethy vijayakumar   9 years AGO

1/[1+(1/a^m-n)]+1/[1+a^m-n]
=(a^m-n)+1/(a^m-n)+1
=1

Like? Yes (1) | No (1)