A shopkeeper cheats 25% in weight while buying rice and cheats 25% while selling it. If he sells the rice at \(12 \frac{1}{2}\) % profit, then find his net profit percentage. 

Given:

The shopkeeper cheats by giving 25% less weight while buying rice.

He also cheats by selling 25% more weight than what he actually bought.

He sells the rice at a profit of 12.5%.

Calculations:

At the time of buying, shopkeeper does a cheating of 25%

⇒ He buys 125 units at the cost of 100 units

At the time of selling, shopkeeper does a cheating of 25%

⇒ He sells 75 units at the cost of 100 units

Shopkeeper sells his goods at the profit of \(12 \frac{1}{2}\)%

⇒ CP = ₹100 and SP = ₹112.5

    CP            SP

   75             125

   100           112.5

-------------------------

  7500        14062.5

⇒ Profit = 14062.5 - 7500 = 6562.5

⇒ %Profit = (6562.5/7500) × 100 = 87.5%

∴ The profit earned by the shopkeeper is 87.5%.