Question:
A dealer sold a camera for Rs 1080 gaining $\frac{1}{8}$ of its cost price. Find
(i) the cost price of the camera, and (ii) the gain per cent earned by the dealer.
Solution:
SP of the camera $=$ Rs. 1080
Let Rs $x$ be the CP.
Gain $=$ Rs. $\frac{1}{8} x \quad \ldots(\mathrm{i})$
Also, gain $=\mathrm{SP}-\mathrm{CP}$
$=$ Rs. $(1080-x) \quad \ldots$ (ii)
From (i) and (ii), we have :
$\frac{1}{8} x=1080-x$
$\Rightarrow x=8640-8 x$
$\Rightarrow 9 x=8640$
$\Rightarrow \mathrm{x}=960$
$\therefore \mathrm{CP}=$ Rs. 960
Now, gain $=\frac{1}{8} \mathrm{x}$
$=\frac{960}{8}$
$=$ Rs. 120
$\therefore$ Gain percentage $=\left(\frac{120}{960} \times 100\right) \%$
$=12 \frac{1}{2} \%$