Question

A shopkeeper gives a discount of $25\%$ on the marked price of an article and still earns a profit of $20\%$ on his outlay. If he had not given any discount, then the profit on his outlay would have been

• A. $45\%$
• B. $50\%$
• C. $55\%$
• D. $37.5\%$

Answer 1

The correct option is D $37.5\%$

Let the $M.P=x$.

discount $=25$%

$S.P=M.P(1-\frac{discount}{100})$

$=x(1-\frac{25}{100})$

$=\frac{3x}{4}$

We know,

$S.P=C.P(1+\frac{profit}{100})$

$\Rightarrow C.P=\frac{S.P}{(1+\frac{profit}{100})}$

$=\frac{\frac{3}{4}}{(1+\frac{20}{100})}$

$=\frac{3x}{4}\times \frac{5}{6}$

$=\frac{5x}{8}$.

It no. discount is given, $S.P=M.P$

$\Rightarrow S.P=x$.

$\therefore$ Profit $=x-\frac{5x}{8}$

$=\frac{3x}{8}$

$\therefore$ Profit % $=\frac{\frac{3x}{8}\times 100}{x}=37.5$%