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

\[\text { Let the cost price of the first box be Rs . x } . \]

\[\text { Therefore, the cost of the second box will be Rs } . (1300 - x)\]

\[\text { Profit on the first box = 20 %} \]

\[\text { Loss on the second box = 12 % } \]

\[\text { SP of the first box = C }P\left( \frac{\text { gain %} + 100}{100} \right)\]

\[SP = x\left( \frac{120}{100} \right)\]

\[\text { SP of the first box = Rs } . \frac{120x}{100} = Rs . \frac{6x}{5}\]

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

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

\[\text { Since S . P of both the box are equal }, \]

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

\[150x = 143000 - 110x\]

\[260x = 143000\]

\[x = \frac{143000}{260}\]

\[x = 550\]

\[\text { Therefore, the cost price of the first box is Rs . 550 }. \]

\[\text { The cost price of the second box will be Rs } . (1300 - 550) = Rs . 750\]