Question

Ramesh bought two boxes for $Rs1300$. He sold one box at a profit of $20\%$ and the other box at a loss of $12\%$.​
If the selling price of both boxes is the same, find the cost price of each box.​

Answer 1

Given that the C.P. of two boxes is $Rs1300$ and he sold first at $20\%$ profit and the other at $12\%$ loss. S.P. of both the boxes is the same.

Let the C.P. of the first box be $\text{x}$ and C.P.of the other be $(1300-\text{x})$
The first box is sold at $20\%$ profit.

$\text{S.P.}=\text{C.P.}\times (1+\frac{\text{\% profit}}{100})$

$=\text{x}\times (1+\frac{20}{100})$

$=\frac{120\text{x}}{100}$

The other table is sold at $12\%$ loss.

$\text{S.P.}=\text{C.P.}\times (1-\frac{\text{\% loss}}{100})$

$=(1300-\text{x})\times (1-\frac{12}{100})$

$=(1300-\text{x})\times \frac{88}{100}$

$\because \text{S.P. of first box}=\text{S.P. of the other box}$

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

$\Rightarrow 120\text{x}=(1300-\text{x})\times 88$

$\Rightarrow 120\text{x}+88\text{x}=1300\times 88$

$\Rightarrow 208\text{x}=1300\times 88$

$\Rightarrow \text{x}=\frac{1300\times 88}{208}=550$

$\text{Now},(1300-\text{x})=(1300-550)=750$

Hence, the cost price of the both the tables are $Rs550$ and $Rs750$ respectively.