A man purchases three objects of consecutive prices. The number of purchased objects are 1, 2 & 3. H

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15 Jan 2014 Solve

A man purchases three objects of consecutive prices. The number of purchased objects are 1, 2 & 3. He pays Rs 115 to shopkeeper. If all prices are taken in integers, then out of 10 choices, the price of that object, whose 3 pieces are purchased, is

OPtion

1) 18
2) 17
3) 21
4) 22
5) 24
6) 20
7) 16
8) 26
9) 12
10)28

Solution

6 cases arise
1x + 2(x + 1) + 3(x + 2) = 115 => x not equal integers
1x + 3(x + 1) + 2(x + 2) = 115 => x = 18
2x + 1(x + 1) + 3(x + 2) = 115 => x = 18
2x + 3(x + 1) + 1(x + 2) = 115 => x not equal integer
3x + 1(x + 1) + 2(x + 2) = 115 => x not equal integer
3x + 2(x + 1) + 1(x + 2) = 115 => x not equal integer
Since x = 18, hence solutions are 19 & 20 according to 2nd and 3rd conditions given above,
Out of 10 choices, 20 is correct

Correct Option: 6 Best Solution (28)

Dr.Dipin Singh   11 years AGO

18*2+19*1+20*3= 36+19+60=115
so the price of that object, whose 3 pieces are purchased, is Rs 20.

Like? Yes (8) | No (5)  

somashekhar   11 years AGO

18*2->36
19*1->19
20*3->60
-->115
So, option # 6 is the right answer

Like? Yes (1) | No   

SHIKHA SUMAN   11 years AGO

let prices of three objects be x, x+1, x+2
now x+2(x+1)+3(x+2)=115
=> 6x + 8= 115
=> x = 17.833
=18
x+2=18+2=20

Like? Yes (1) | No   

ramakrishna   11 years AGO

Object prices are consecutive so,
Let we take ,the prices as
X,X+1,X+2
The number of purchased objects are 1,2,3
so,
X+2(X+1)+3(X+2)=115
X+2X+2+3X+6=115
6X+8=115
6X=115-8
X=107/6
X=17.8(appx 18)
All are taken in Integers so ,prices are
18,19,20
he asked 3 Pieces object price so answer is 20
Option 6 is answer

Like? Yes (1) | No   

Dayashankar Rajhans   11 years AGO

2x+(x+1)+3(x+2)=115
so,x=18
and,x+2=20

Like? Yes (1) | No   

Satya   11 years AGO

let the price are like x,x+1 and x+2
so he will purchase like 3 objects from price of x+2
2 objects from price of x
and 1 object from price of x+1

so the eqn becomes 3(x+2)+2(x)+(x+1)=115
=> 3x+6+2x+x+1=115
=>6x=108
=>x=18

as the man purchased 3 objects from price of x+2 .so the ans is 20

Like? Yes (4) | No (6)  

Udhaya kumar   11 years AGO

x+2(x+1)+3(x+2) = 115
x=17.8
ans x+2 = 19.8 = 20.......

Like? Yes (3) | No (6)  

DHIRENDRA    11 years AGO

let three consicutive price are
x,x+1,x+2
given
The number of purchased objects are 1, 2 & 3. He pays Rs 115
x+2(x+1)+3(x+2)=115
x+2x+2+3x+6=115
6x+8=115
6x=115-8
x=107/6
x=17.833333
x=18(approximate)
then

1 objects price =18
2 objects price =19
3 objects price =20

Like? Yes (1) | No (4)  

KRISHNAN   11 years AGO

Let x be the price of First object
then 2 object will be x +1 and 3 rd object x + 2

So x + 2(x+1) + 3(x+2) = 115
or 6x = 107
0r x = 17.83 or 18
so price of 3 object bought is 18+2 or 20

Like? Yes (1) | No (5)  

Vinay Sipani    11 years AGO

Let the prices of objects be (x-1),x,(x+1)

Let no. of pieces of each objecg that was purchased be a,b,c
where a,b,c = 1,2,3 (not in ordered form)

=> a(x-1) + bx + c (x+1) = 115
=> x (a+b+c) + (c-a) = 115

a+b+c=6 => 6x = 115 - (c - a)

The RHS must be even to be divisible by 6
=> (c-a) must be odd

114 is divisible by 6 => (c - a) = 1
=> c,a = (3,2) or (2,1)

1) If (a,b,c) = (2,1,3) => x = 19
=> The price of object with 3 pieces = 20

2) If (a,b,c) = (1,3,2) => x= 19
=> The price of object with 3 pieces = 19

So possible answers are Rs.19 and Rs.20
=> Option 6

Like? Yes (2) | No (6)  

Naveen Pandey   11 years AGO

ITS EASY :)

Like? Yes (1) | No (5)  

Vijay Chauhan   11 years AGO

he purchase,
1 for 19
2 for 18 and
3 for 20.....

Like? Yes (2) | No (6)  

Krishna Chaitanya   11 years AGO

Given a man purchases three objects of consecutive prices. The number of purchased objects are 1, 2 & 3. He pays Rs 115 to shopkeeper.
From the given option let the 3rd object price be Rs 20 then 2nd object price is Rs 19 and 1st object price is Rs 18.
Therefore total price of three objects=18+2(19)+3(20)=116 which is nearly equal to 115.

Like? Yes (2) | No (6)  

satyen nabar   11 years AGO

Let n be price of the cheapest item
So (n+1) and (n+2) are the prices of the other 2 items.
The only equation that gives n as a whole integer is
2n + (n+1) + 3(n+2)= 115.
6n+7 =115.
n= 18.
Price of item whose 3 pieces are purchased is 20.

Like? Yes (2) | No (6)  

Chandni Maurya   11 years AGO

ans=20
20*3+18*2+19=115

when we assume consecutive prices of purchased object 1,2,3 resp. then it must be even
as (x-2)+2(x-1)+3x or (x+2)+2(x+1)+3x is always even whether x is even or odd .

so,
again lets assume x is the price of 3rd object
and 2,1,3 resp are in consecutive prices
(x-1)+2(x-2)+3x =115
6x-5=115
x=120/6=20

Like? Yes (2) | No (6)  

madanpal vishwakarma    11 years AGO

let the first object price is x
then second should be x+1
and next x+3
so
according to the problem
x+(x+1)*2+(x+2)*3=115
so after solving
x=18
so
3rd object price is
x+2=18+2=20

Like? Yes (3) | No (7)  

ASHISH MITTAL   11 years AGO

x+2(x+1)+3(x+2)=115
x+2x+2+3x+6=115
6x=115-8
x=107/6
18(approx)
so with 3 piece object price would be 18+2=20

Like? Yes (2) | No (6)  

pankaj chandra joshi   11 years AGO

let first price =x
2nd is x+1
3rd is x+2
1st purchased
+1peace 2nd 2,3rd 3
totel paid =115
x+2(x+1)+3(x+2)=115
x=17.8
18
so x+2=19.8
20 approx
option 6

Like? Yes (1) | No (5)  

swastik   11 years AGO

let the price are like x,x+1 and x+2
so he will purchase like 3 objects from price of x+2
2 objects from price of x
and 1 object from price of x+1

so the eqn becomes 3(x+2)+2(x)+(x+1)=115
=> 3x+6+2x+x+1=115
=>6x=108
=>x=18

as the man purchased 3 objects from price of x+2 .so the ans is 20

Like? Yes (4) | No (8)  

mahima srivastava   11 years AGO

the prices will be x, x+1, x+2
quantity is 1, 2 and 3

x+2(x+1)+3(x+2)=115
x=17.333
but it is not an integer value

now next equation can be,
2x+x+1+(x+2)3=115
x=18
the object whose three pieces are purchased is of price x+2
so its price is 20

Like? Yes (1) | No (5)  

upendra singh chahar   11 years AGO

3(x)+2(x-1)+(x-2)=115
here x will not an integer.
so other choice is 3(x)+(x-2)+2(x-1)=115
after solving
x=20

Like? Yes (1) | No (5)  

VIKASH RAY   11 years AGO

Let, the prices of the three integer is-(x-2),(x-1),x.
then,
price of first object is-(x-2)
price of 2nd object is-2(x-1)
price of 3rd object is-3(x)
according to question,
(x-2)+2(x-1)+3(x)= 115
=> x=19.833333
=20 (appx.)
so, option 6 is correct.

Like? Yes (1) | No (5)  

Devendra Marghade   11 years AGO

If prices of three objects are x,(x+1),(x+2) then
x+2(x+1)+3(x+2)=115
6x+8=115, x=107/6
the price of that object, whose 3 pieces are purchased=(107/6)+2=119/6=19.833=20 approx.

Like? Yes (1) | No (5)  

sudipta sadhukhan   11 years AGO

18*2+19*1+20*3=115

Like? Yes (3) | No (7)  

Ramneek    11 years AGO

let the prices of 3 obejcts be
x,x+1,x+2 and the number of objects purchased in order 2,1,3 resp

2x+(x+1)+3(x+2)=115
x=18
price of that object, whose 3 pieces are purchased, is
x+2=20

Like? Yes (3) | No (7)  

B.Senthil Kumar   11 years AGO

x+2x+2+3x+3=115
6x+5=115
6x=110
x=18.3 so approximately 18 and answer is 20 i.e. x+2

Like? Yes (1) | No (5)  

susmit   11 years AGO

1*x+2*(x+1)+3*(x+2)=115
solving x=18 (near integer)
x+2=20
option no.6

Like? Yes (1) | No (6)  

Akanksha Mishra   11 years AGO

Consider purchases three objects of consecutive prices are x,(x+1),(x+2)

According to the question
The number of purchased objects are 1, 2 & 3

so prices of that object x , 2(x+1) , 3(x+2)

Total cost = 115 Rs

x + 2(x+1) + 3(x+2) = 115
x + 2x +2 + 3x + 6 = 115
6x + 8 = 115
6x = 107
x = 107/6
x = 17.833
he price of that object, whose 3 pieces are
= (x+2) = 17.833 + 2 = 19.833
prices are taken in integer no.
so ans will 20(option 6)

Like? Yes (15) | No (20)