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 amound for each fan, find the cost price of each fan.

Answer 1

Total cost price of two fans = Rs. 3605
Let selling price of each fan = Rs. 100
Now, S.P of first fan = Rs. 100
Profit $=15\%$
$\therefore$ C.P $=\frac{S.P\times 100}{100+profit\%}=Rs.\frac{100\times 100}{100+15}$
$=Rs.\frac{10000}{115}$
S.P of the second fan = Rs. 100
Loss $=9\%$
$\therefore$ C.P $=\frac{S.P\times 100}{100-loss\%}=Rs.\frac{100\times 100}{100-9}$
$=Rs.\frac{10000}{91}$
$\therefore$ Ratio in their C.P's $=\frac{10000}{115}:\frac{10000}{91}$
$=\frac{1}{115}:\frac{1}{91}=91:115$
Sum of ratio's = 91+115 = 206
$\therefore$ C.P of first fan $=Rs.\frac{3605\times 91}{206}$
=Rs. 1592.50
and C.P of second fan $=Rs.\frac{3605\times 115}{206}$
=Rs. 2012.50