Question

A reduction of $25\%$ in the price of an article enables a man to buy $50$ kilograms more for Rs. $500$. What is the reduced price per kilogram?

• A. Rs. $3$
• B. Rs. $2.50$
• C. Rs. $2.05$
• D. Rs. $2.40$

Answer 1

Answer: (B)

Rs. $2.50$

Let the original price per kg of the article be Rs. $x$.

Then the reduced price per kg $=\frac{75}{100}\times$ Rs. $x=$ Rs.$\frac{3x}{4}$
Amount of article that can be bought for Rs. $500$ originally $=\frac{500}{x}$ kg
Amount of article that can be bought for Rs. $500$ by reduced price $=\frac{500}{3x/4}$ kg $=\frac{500\times 4}{3x}$ kg
Given, $\frac{500\times 4}{3x}=\frac{500}{x}+50$

$\Rightarrow \frac{2000-1500}{3x}=50$

$\Rightarrow \frac{500}{3x}=50$
$\Rightarrow x=\frac{500}{50\times 3}=$ Rs. $\frac{10}{3}$

$\therefore$ Reduced price $=\frac{3}{4}\times$ Rs. $\frac{10}{3}=$ Rs. $2.50$