M4maths Previous Puzzles

13 Apr 2016 Which option is correct

Suppose b varies as the sum of two quantities of which one varies directly as a and the other inversely as a.
If b=6 when a=4 and b=10/3 when a=3, then which option is correct.

OPtion

1) b = 4a - 1/a
2) b = 2a - 3/a
3) b = a - 1/a
4) b = 7a - 8/a
5) b = 5a - 8/a
6) b = 2a - 8/a
7) b = 2a - 9/a
8) b = 2a - 1/a
9) b = a - 8/a
10)None of these

Solution

By using Ration and proportion
Let b = x+y where x => a and y => 1/a
Let x = k1 a and y = k2/a where k1 and k2 are constant
therefore
b = k1 a + k2/a
By using given value find k1 and k2
Putting the values we get
b = 2a - 8/a
Option 6)

Correct Option: 6 Best Solution (27)

priti kiran   8 years AGO

suppose two quantities are x and y.
x varies directly as a.
y varies inversely as a.
so, b=x+y
i.e b=c1*a+c2/a
where c1 and c2 are constants.
At 1st
b=6 and a=4
so,
4c1+c2/4=6 eqn-----(1)

At 2nd
b=10/3 and a=3
so,
3c1+c2/3=10/3 eqn----(2)
Now, solving eqn--(1) and eqn--(2)
we get,
c1=2 & c2=-8
so, solution is
b=2a-8/a

Like? Yes (2) | No   

Vivek Ratan   8 years AGO

create two equations having constants k1 and k2 with the given values and solve them each to find value of k1 and k2.

On putting the values of k1 and k2 , we get b=2a-8/a as answer.

Like? Yes (1) | No   

mcamanjeet   8 years AGO

according to question
b = t + m ( sum of two number )
and a/question t is directly proportional to a and m is inversely proportional to a
that is t = k . a and m = p/a where k , p are proportional constant
equation becomes
b = k .a + p/a .........................................equ 1
for two different value of a , b
b = 6 ,a = 4
we get
6 = 4k + p/4
16k + p = 24 ....................... 2nd equation
similarly if we put
b = 10/3 ,a = 3
then the equ become 9k + p = 10 ........ 3rd equation
now solving 1 and 2 we get
k = 2 and p = - 8
putting these value in 1st
we get ans b = 2a - 8/a

Like? Yes (1) | No   

Mukund Manohar   8 years AGO

Let b (dp) p+q where p (dp) a and q (ip) 1/a
So, b=K(p+q)
p=Ma , q=N/a
=> b=K(Ma + N/a)
b=10/3 when a = 3
=> K(3M + N/3) = 10/3
So,MK=2 and NK= -8
So,p=2a/K and q = -8/Ka
Hence,b= 2a - 8/a ----------option (6)

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THUMMALA VINEESHA   8 years AGO

b=a+(1/a)
given b=6 and a=4,
6=4+(1/4), it does not satisfy
also given b=10/3 and a=3
10/3=3+(1/3), it satisfies
so b=10/3 and a=3
now option checking
6)option
b=2a-(8/a)
10/3=2(3)-(8/3)=6-(8/3)=(18-8)/3=10/3
so option6)

Like? Yes (1) | No (1)  

MRITUNJAY   8 years AGO

A. x = y+4 
B. y = 2x+(8/x) 
c. y = 2x-(8/x) 
D. y = 2x-(4/x)

y = ax + b/x 
6 = 4a + b/4 ___ (1) 
10/3 = 3a + b/3 ___ (2) 
from (1) 24 = 16a + b 
from (2) 10 = 9a + b 
14 = 7a 
a = 2 
b = -8 

y = 2x - 8/x 

option 6

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RAHUL KUMAR   8 years AGO

b = xa + y/a
6 = 4x + y/4 ___ (1)
10/3 = 3x + y/3 ___ (2)
from (1) 24 = 16x + y
from (2) 10 = 9x + y
from (1) - (2), We get,
14 = 7x
x = 2
y = -8
b = 2a - 8/a
option (6)

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ABHINAV PUSHPAM   8 years AGO

y = ax + b/x
6 = 4a + b/4 ___ (1) 
10/3 = 3a + b/3 ___ (2) 
from (1) 24 = 16a + b 
from (2) 10 = 9a + b 
14 = 7a 
a = 2 
b = -8 

b= 2a -8/a.

Option 6)

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Yashi Das   8 years AGO

when a=4 then y=6
putting a=4 in all the options we get that only
b=2 a-(8/a) yields b=6
therefore option 6) is correct

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RISHABH   8 years AGO

b=ax+y/a
6= 4x +y/4
=> 24=16x+y.........(1)
Also, 10/3=3x+y/3
=> 10=9x+y........(2)
From (1) & (2)
14=7x
=> x=2
and y= -8
So, b= 2a - 8/a

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Maji   8 years AGO

When a=4 ,
b=2a-8/a=2 (4)-8/4=8-2=6.
when a=3,
b=2a-8/a
=2 (3)-8/3=6-8/3=18-8/3=10/3.
Therefore,

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Imtha thullah   8 years AGO

When a=4,
b=2a-8/a,
b=2 (4)--8/4=8-2=6,
therefore,
option :)6

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Ambica Mehrotra    8 years AGO

b= q1 + q2
q1 = m1 * a
q2 = m2/a
b= m1*a + m2/a
when b= 6 then a= 4
and when b= 10/3 a=3
4*m1 + m2/4 = 6
3* m1 + m1*3 = 10/3
solving both equations we get m1=2 , m2= -8
so.. b= 2a - 8/a

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Lenin   8 years AGO

substitute the values of a=4 & a=3 in option 6.
you will get the given b values.

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rydham goyal   8 years AGO

if we put the value of a in eq 6
b = 2*4 - 8/4
b=8-2
b=6

and

b=2*3 - 8/3
b=6- 8/3
b=18-8/3
b=10/3
hence proved

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palak tandon   8 years AGO

at b=6 and a=4
at b=10/3 and a=3 which satisfies option 6

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sugayathri   8 years AGO

check the options and put a=4 and 3
get b value is correct

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Kalpana   8 years AGO

substitute the given questions in the options
when a=4 and a=3 is substituted in the 2a-8/a we get b=6 and b=10/3

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Akshat Sood   8 years AGO

b=a+1/a
By hit and trial method
we get and as 2a-8/a

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madanpal vishwakarma    8 years AGO

as given b=6 when a=4 and b=10/3 when a=3

so lets put these values on option list

take option 6
b=2a-8/a
if put a=4 then you will get b=6
and if you put a=3 then you'll get b=10/3

so option 6 is correct

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Juned A Hashmi   8 years AGO

On putting value a = 4 and 3, we get b = 6 and 10/3 from option 6 only.

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GREAT GAURAV   8 years AGO

put the value a=3 in option 6 and the value of b will come 10/3

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Anish Singh Dhami   8 years AGO

by substituting the value of a in equation 6 it satisfied both the condition.

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Akhilesh kumar   8 years AGO

in option (6) we putting value of a=4 and 3 we get value of b is 6 and 10/3 respectively...

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Sujoy bhuin   8 years AGO

Because of b=10/3 and a=3 then option 6) is right
When ,b=2a-8/a

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priyanka   8 years AGO

a=4
b=2*4-8/4=6
a=3
b=2*3-8/3=10/3

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jagan mohan reddy   8 years AGO

Option method
6 option is suitable
B=2a-8/a

B=2(4)-8/4=6
B=2(3)-8/3=10/3

Like? Yes | No