A reduction of 21 % in price of an item enables a person to buy 3, Kg more for Rs.,100. reduced pric

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7.Profit and Loss

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A reduction of $21 \%$ in the price of an item enables a person to buy $3\, Kg$ more for $Rs.\,100.$ The reduced price of the item per $Kg$ is (in $Rs.$)

A

$5.50$

B

$7.50$

C

$10.50$

D

$7.00$

Solution

Let, the original price of the article be $₹ x$ per $Kg$.

$\therefore \quad$ New price $=₹ \frac{79 x}{100}$ per $Kg$

Now, according to the question,

$\frac{100}{\frac{79 x}{100}}-\frac{100}{x}=3$

$\Rightarrow \frac{10000}{79 x}-\frac{100}{x}=3$

$\Rightarrow \frac{10000-7900}{79 x}=3$

$\Rightarrow \frac{2100}{79 x}=3$

$\Rightarrow \frac{700}{79 x}=1$

$\Rightarrow \quad 79 x=700 \Rightarrow x=\frac{700}{79}$

$\therefore \quad$ New price $=\frac{79 x}{100}=\frac{79}{100} \times \frac{700}{79}=Rs. 7$ per $Kg$

Standard 13

Quantitative Aptitude

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