A reduction of 25% in the price of an article enables a man to buy 50

1.	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» (b) Rs 2.50 Let the original price per kg of the article be Rs x. Then, the reduced price per kg = \(\frac{75}{100}\) x 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 = \(\frac{500}{\frac{3X}{4}}\) kg = \(\frac{500\times4}{3X}\)kg Given, \(\frac{500\times4}{3X}\) = \(\frac{500}{X}\) + 50 \(\Rightarrow\) \(\frac{2000-1500}{3X}\) = 50 \(\Rightarrow\) \(\frac{500}{3X}\) = 50 \(\Rightarrow\) x = \(\frac{500}{50\times3}\) = Rs \(\frac{10}{3}\) \(\therefore\) Reduced price = \(\frac{3}{4}\) x Rs \(\frac{10}{3}\) = Rs 2.50

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»

(b) Rs 2.50

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

Then, the reduced price per kg = \(\frac{75}{100}\) x 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 = \(\frac{500}{\frac{3X}{4}}\) kg = \(\frac{500\times4}{3X}\)kg

Given, \(\frac{500\times4}{3X}\) = \(\frac{500}{X}\) + 50

\(\Rightarrow\) \(\frac{2000-1500}{3X}\) = 50

\(\Rightarrow\) \(\frac{500}{3X}\) = 50

\(\Rightarrow\) x = \(\frac{500}{50\times3}\) = Rs \(\frac{10}{3}\)

\(\therefore\) Reduced price = \(\frac{3}{4}\) x Rs \(\frac{10}{3}\) = Rs 2.50