​ A reduction of 20% in the price of sugar enables a purchaser to obtain 2(1/2)kg more for Rs 160. Find the original price per kg of sugar. ​

Question

A reduction of 20% in the price of sugar enables a purchaser to obtain 2\(\frac{1}{2}\) kg more for Rs 160. Find the original price per kg of sugar.

Answer 1

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

Then, the reduced price per kg = Rs \(\frac{4X}{5}\)

Quantity of sugar that can be bought for Rs 160 originally = Rs \(\frac{160}{X}\)

Quantity of sugar that can be bought for Rs 160 with reduced price = Rs \(\frac{160}{\frac{4X}{5}}\) = 160 x \(\frac{5}{4X}\)

Given, 160 x \(\frac{5}{4X}\) = \(\frac{160}{X}\)+ \(\frac{5}{2}\) \(\Rightarrow\) x = 16

\(\therefore\) Original price per kg = Rs 16.