A shopkeeper sold an item at 10 % loss after giving a discount equal to half marked price. cost pric

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7.Profit and Loss

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A shopkeeper sold an item at $10 \%$ loss after giving a discount equal to half the marked price. The cost price of the item is......... of marked price

A

$\frac{1}{9}$

B

$\frac{4}{9}$

C

$\frac{5}{9}$

D

$\frac{7}{9}$

Solution

Let, the marked price and the cost price be $₹ x$ and $₹y,$ respectively.

Now, according to the question,

$50 \%$ of $x=90 \%$ of $y$

$\Rightarrow \frac{x \times 50}{100}=\frac{y \times 90}{100}$

$\Rightarrow y=\frac{x \times 50}{90}=₹ \frac{5}{9} x$

$=\frac{5}{9}$ of the marked price.

Standard 13

Quantitative Aptitude

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