If cost price of an item is frac{2}{5} of its marked price and if it is sold at a discount of 10 %,

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7.Profit and Loss

medium

If the cost price of an item is $\frac{2}{5}$ of its marked price and if it is sold at a discount of $10 \%,$ then there will be

A

$25 \%$ profit

B

$40 \%$ profit

C

$50 \%$ profit

D

$125 \%$ profit

Solution

Let, the marked price of article be $₹ x$

Now, according to the question,

$\therefore \quad$ $C.P.$ of article $=₹ \frac{2 x}{5}$

$S.P.$ of article $=\frac{x \times 90}{100}=₹ \frac{9 x}{10}$

Gain $=\frac{9 x}{10}-\frac{2 x}{5}=\frac{9 x-4 x}{10}=\frac{5 x}{10}=\frac{x}{2}$

$\therefore \quad$ Gain percent $=\frac{\operatorname{Gain} \times 100}{\text { C.P. }}$

$=\frac{\frac{x}{2} \times 100}{\frac{2 x}{5}}=\frac{5 \times 100}{4}=125 \%$

Standard 13

Quantitative Aptitude

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