# Mariam bought two fans for Rs 3605.

Question:

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:

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. $2012.50$