By selling an umbrella for Rs., 300, a shopkeeper gains 20 % . During a clearance sale, shopkeeper a

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7.Profit and Loss

hard

By selling an umbrella for $Rs.\, 300,$ a shopkeeper gains $20 \%$. During a clearance sale, the shopkeeper allows a discount of $10 \%$ on the marked price. His gain per cent during the sale is

A

$7$

B

$7.5$

C

$8$

D

$9$

Solution

$S.P.$ $=$ $C.P.$ $\left(1+\frac{x}{100}\right)$ where $x$ is profit $\%$

$\therefore \quad 300= C \cdot P \cdot\left(1+\frac{20}{100}\right)$

or $C.P. =\frac{300}{1.2}=Rs. 250$

After discount, $S.P.$ $=300 \times\left(1-\frac{10}{100}\right)=Rs. 270$

$\therefore \quad \operatorname{Gain} \%=\frac{ S.P. – C.P. }{ C.P. } \times 100$

$=\frac{270-250}{250} \times 100=8 \%$

Standard 13

Quantitative Aptitude

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