Question:
Meenakshi sells a pen for Rs 54 and loses $\frac{1}{10}$ of her outlay. Find (i) the cost price of the pen, and (ii) the loss per cent.
Solution:
SP of the pen $=$ Rs. 54
Let Rs $x$ be the CP of the pen.
Loss $=$ Rs. $\frac{x}{10}$
$\mathrm{SP}=\mathrm{CP}-$ Loss
$=x-\frac{x}{10}$
$=$ Rs. $\frac{9 x}{10}$
Now, we have $\frac{9 \mathrm{x}}{10}=54$
$\Rightarrow x=54 \times \frac{10}{9}$
$\Rightarrow \mathrm{x}=60$
$\therefore$ CP of the pen $=$ Rs. 60
Now, loss $=\frac{\mathrm{x}}{10}$
Now, loss $=\frac{x}{10}$
$=\frac{60}{10}$
$=\operatorname{Rs} .6$
$\therefore$ Loss percentage $=\left(\frac{\text { loss }}{\mathrm{CP}} \times 100\right) \%$
$=\left(\frac{6}{60} \times 100\right) \%$
$=10 \%$