Mariam bought two fans for Rs 3605. She sold one at a profit of 15% and the other at a loss of 9%. If Mariam obtained the same amount for each fan, find the cost price of each fan.

#### Solution

\[\text { It is given that the S . P is same for both the fans } . \]

\[\text { Let C . P of the first fan be Rs . x }\]

\[\text { Therefore, C . P of the second fan = Rs }. (3605 - x)\]

\[\text { Profit on the first fan = 15 % } \]

\[\text { Loss on the second fan = 9 % } \]

\[\text { For the first fan }, \]

\[\text { S . P = C . P }\left( \frac{100 + \text { gain % }}{100} \right)\]

\[ = x\left( \frac{115}{100} \right)\]

\[ = \frac{23x}{20}\]

\[\text { For the second fan }, \]

\[\text { S . P = C . P }\left( \frac{100 -\text { loss % }}{100} \right)\]

\[ = \left( 3605 - x \right)\left( \frac{91}{100} \right)\]

\[\text { Since S . P of both the fans is the same, } \]

\[\frac{23x}{20} = \left( 3605 - x \right)\left( \frac{91}{100} \right)\]

\[2300x = 91\left( 72100 - 20x \right)\]

\[2300x = 6561100 - 1820x\]

\[4120x = 6561100\]

\[x = Rs . 1592 . 50\]

\[\text { Thus, C . P of the first fan is Rs } . 1592 . 50 . \]

\[\text { C . P of the second fan = Rs } . \left( 3605 - 1592 . 50 \right)\]

\[ = Rs . 2012 . 50\]