A shopkeeper bought 120 quintals of wheat. 20% of it was sold at 25% loss. At what percent gain should he sell the rest to gain 25% on the whole transaction?

Solution (By Examveda Team)

Quantity of wheat bought by shopkeeper = 120
Let the price of the 120 quintals of wheat = Rs. 120
According to the question
$$\eqalign{ & 120 \times \frac{1}{5} \times \frac{{75}}{{100}} + 120 \times \frac{4}{5} \times \frac{{100 + x}}{{100}} = 120 \times \frac{{125}}{{100}} \cr & \Rightarrow 18 + \frac{{24}}{{25}} \times \left( {100 + x} \right) = 150 \cr & \Rightarrow \frac{{24}}{{25}} \times \left( {100 + x} \right) = 150 - 18 \cr & \Rightarrow \frac{{24}}{{25}} \times \left( {100 + x} \right) = 132 \cr & \Rightarrow 100 + x = 132 \times \frac{{25}}{{24}} \cr & \Rightarrow 100 + x = 137.5 \cr & \Rightarrow x = 137.5 - 100 \cr & \Rightarrow x = 37.5\% {\text{ or }}37\frac{1}{2}\% \cr} $$