Question

A shopkeeper sold an article at a gain of $5\%$. If he had sold it for $Rs.16.50$ less, he would have lost $5$. Find the cost price of the article.

Answer 1

Let the Cost price be $Rs.x$

Profit $=Rs.\frac{5x}{100}$

$\therefore$ Selling price $=Rs.\frac{105x}{100}$

New selling price $=Rs.(\frac{105x}{100}-16.50)$

Loss $=Rs.(x-\frac{105x}{100}+16.50)$

$\Rightarrow 5=x-\frac{105x}{100}+16.50$

$\Rightarrow 5-16.50=\frac{100x-105x}{100}$

$\Rightarrow -11.50=\frac{-5x}{100}$

$\Rightarrow 11.50=\frac{5x}{100}$

$\Rightarrow 11.50\times 100=5x$

$\Rightarrow 1150=5x$

$\Rightarrow \frac{1150}{5}=x$

$\Rightarrow 230=x$

Hence, the Cost price is $Rs.230$