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.
It is given that the $S$. $P$ is same for both the fans.
Let C.P of the first fa $n$ be Rs. $\mathrm{x}$
Therefore, C.P of the second fan $=$ Rs. $(3605-\mathrm{x})$
Profit on the first fan $=15 \%$
Loss on the second fan $=9 \%$
For the first fan,
S.P $=$ C.P $\left(\frac{100+\text { gain } \%}{100}\right)$
$=x\left(\frac{115}{100}\right)$
$=\frac{23 x}{20}$
For the second fan,
S.P $=$ C.P $\left(\frac{100-\text { loss } \%}{100}\right)$
$=(3605-x)\left(\frac{91}{100}\right)$
Since S. P of both the fans is the same,
$\frac{23 x}{20}=(3605-x)\left(\frac{91}{100}\right)$
$2300 x=91(72100-20 \mathrm{x})$
$2300 x=6561100-1820 \mathrm{x}$
$4120 x=6561100$
$x=$ Rs. $1592.50$
Thus, C.P of $t h e$ first fan $i s$ Rs. $1592.50 .$
C. P of $t h e$ second fan $=$ Rs. $(3605-1592.50)$
$=$ Rs. $2012.50$