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 difference between the cost price of first and second fan.

Answer 1

Correct option is A. 420

It is given that the $$\mathrm{S.P}$$ is same for both the fans.

Let $$\mathrm{C.P} $$ of the first fan be $$\mathrm{Rs.}\space x$$

$$\therefore \mathrm{C.P}$$ of the second fan $$=\mathrm{Rs.}\space (3605-x)$$

Profit on the first fan $$=15 \%$$

Loss on the second fan $$=9 \%$$

For the first fan,

$$\mathrm{S.P}=\mathrm{C.P}\left(\frac{100+\mathrm{Gain} \%}{100}\right)$$

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

$$=\frac{23 x}{20}$$

For the second fan, $$\mathrm{S.P}=\mathrm{C.P}\left(\frac{100-\mathrm{Loss} \%}{100}\right)$$

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

Since $$\mathrm{S.P}$$ of both the fans is the same,

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

$$\Rightarrow 2300 x=91(72100-20 x)$$

$$\Rightarrow 2300 x=6561100-1820 x$$

$$\Rightarrow 4120 x=6561100$$

$$\Rightarrow x=\mathrm{Rs.} \space1592.50$$

Thus, $$\mathrm{C.P}$$ of the first fan is $$\mathrm{Rs.} \space1592.50$$ .

$$\mathrm{C.P}$$ of the second fan $$=\mathrm{Rs.}\space (3605-1592.50)=\mathrm{Rs.} \space2012.50$$
difference between the cost price of first and second fan $$=2012.50-1592.50=\text{Rs}\,420$$