Ramesh bought two boxes for Rs 1300.
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.

Solution:

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

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

Profit on the first box $=20 \%$

Loss on the second box $=12 \%$

$\mathrm{SP}$ of the first box $=\mathrm{CP}\left(\frac{\text { gain } \%+100}{100}\right)$

$\mathrm{SP}=\mathrm{x}\left(\frac{120}{100}\right)$

$S P$ of the first box $=$ Rs. $\frac{120 x}{100}=$ Rs. $\frac{6 x}{5}$

SP of the second box $=\operatorname{CP}\left(\frac{100-\text { loss } \%}{100}\right)$

$S . \mathrm{P}$ of the second box $=\frac{88(1300-x)}{100}=$ Rs. $\left(\frac{28600-22 x}{25}\right)$

Since $S$. P of both the box are equal,

$\frac{6 x}{5}=\left(\frac{28600-22 x}{25}\right)$

$150 x=143000-110 x$

$260 x=143000$

$x=\frac{143000}{260}$

$x=550$

Therefore, the cost price of the first box is Rs. 550 .

The cost price of the second box will be Rs. $(1300-550)=$ Rs. 750