Question:
The cost price of 12 candles is equal to the selling price of 15 candles. Find the loss per cent.
Solution:
Let Rs $x$ be the CP of one candle and Rs. $y$ be the SP of one candle.
Now, $\mathrm{CP}$ of 12 candles = SP of 15 candles
$\Rightarrow 12 x=15 y$
$\Rightarrow \frac{y}{x}=\frac{12}{15}$
Loss $=\mathrm{CP}-\mathrm{SP}$
$=\mathrm{Rs}(x-y)$
$\therefore$ Loss percentage $=\left(\frac{\text { loss }}{\mathrm{CP}} \times 100\right) \%$
$=\left\{\left(\frac{x-y}{x}\right) \times 100\right\} \%$
$=\left\{\left(1-\frac{y}{x}\right) \times 100\right\} \%$
$=\left\{\left(1-\frac{12}{15}\right) \times 100\right\} \%$
$=\left(\frac{3}{15} \times 100\right) \%$
$=20 \%$