Question

Ramesh bought two boxes for $Rs.1300$. 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

Let the cost price of the first box be $Rs.x$.

Therefore, the cost of the second box will be $Rs.(1300-x)$

Case 1:

Profit on the first box $=20\%$

SP of the first box $=(100+20)\%\times C.P$

$=\left(120\right)\%\times x$

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

$=\frac{6x}{5}$

So, SP of the first box $=\frac{6x}{5}$ ---(1)

Case 2:

Loss on the second box $=12\%$

SP of the second box $=(100-12)\%\times C.P$

$=\left(88\right)\%\times (1300-x)$

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

So, SP of the second box $=\frac{88(1300-x)}{100}$ ---(2)

It is given that, selling price of both boxes is the same.

$\Rightarrow \frac{88(1300-x)}{100}=\frac{6x}{5}$

$\Rightarrow 5\left(88\right(1300-x\left)\right)=600x$

$\Rightarrow 440(1300-x)=600x$

$\Rightarrow 44(1300-x)=60x$

$\Rightarrow 57200-44x=60x$

$\Rightarrow 57200=60x+44x$

$\Rightarrow 57200=104x$

$\Rightarrow \frac{57200}{104}=x$

$\Rightarrow 550=x$

$\Rightarrow x=550$

Therefore, the cost price of the first box be $Rs.550$.

$\Rightarrow$ the cost price of the first box be $Rs.(1300-550)=Rs.750$.