Shubham bought some chocolates and gave half of them to Saurabh. Saurabh bought some sweets and gave half of them to Shubham. Shubham ate 12 sweets and Saurabh ate 18 chocolates. After that, the number of sweets and chocolates Shubham had were in the ratio 1: 7 and the number of sweets and chocolates Saurabh had were in the ratio 1: 4. How many sweets did Saurabh buy?
(1) 68
(2) 64
(3) 54
(4) 58

Given:

Shubham bought some chocolates and gave half of them to Saurabh. Saurabh bought some sweets and gave half of them to Shubham. Shubham ate 12 sweets and Saurabh ate 18 chocolates. After that, the number of sweets and chocolates Shubham had were in the ratio 1: 7 and the number of sweets and chocolates Saurabh had were in the ratio 1: 4. 

To do:

We have to find the number of sweets bought by Saurabh.

Solution:

Let the number of chocolates bought by Shubham be 2x and the number of sweets bought by Saurabh be 2y.

Number of sweets left with Shubham$=y-12$

Number of chocolates left with Shubham$=x$

Number of sweets left with Saurabh$=y$

Number of chocolates left with Shubham$=x-18$

Therefore,

$y-12:x=1:7$
$\frac{y-12}{x}=\frac{1}{7}$

$7(y-12)=1(x)$

$7y-84=x$.....(i) 

$y:x-18=1:4$

$\frac{y}{x-18}=\frac{1}{4}$

$4(y)=1(x-18)$

$4y=x-18$

$4y=7y-84-18$    (From (i))

$7y-4y=84+18$

$3y=102$

$y=\frac{102}{3}$

$y=34$

$\Rightarrow 2y=2(34)=68$

Number of chocolates bought by Saurabh are 68.

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Updated on: 10-Oct-2022

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