Question

A man bought $2$ boxes for $Rs.1300$. He sold one box at a profit of $20\%$ and another box at a loss of $12\%$ If the selling price of both the boxes is the same find the cost price of the first box sold at a profit of $20\%$:

Answer 1

Let the $CP$ of the first box which was sold at a profit of $20\%$ be $Rs.x.$
Then the $CP$ of the second box which was sold at a loss of $12\%$ will be $Rs.1300-x.$

Since the first box was sold a profit of $20\%$ its,
$SP=Rs.\frac{120}{100}x$

$SP$ of second box $=Rs.\frac{88(1300-x)}{100}$

Since the $SP$ of both the boxes are same we have,

$\frac{120x}{100}=\frac{88(1300-x)}{100}$
$\Rightarrow 15x=11(1300-x)$
$\Rightarrow 15x+11x=11\times 1300$

$\Rightarrow 26x=14300$
$\Rightarrow x=Rs.550$

Hence $CP$ of the first box is equal to $Rs.550$ and that of the second box $Rs.(1300-550)=Rs.750.$