A person bought a certain quantity of rice at the rate of Rs. 250 per quintal.…

Concept

When a trader's stock suffers wastage or spoilage before sale, the desired profit percentage still applies to the entire cost price, but the whole required revenue must be recovered by selling only the surviving (unspoiled) quantity. So the required total revenue = Cost Price × (1 + Profit% / 100), and this amount is divided among the remaining saleable quantity to find the necessary selling rate.

Application

1. Take the purchased quantity as 1 quintal (100 kg), bought at a cost price of Rs. 250.

2. 20% of the rice spoils: 20% of 100 kg = 20 kg spoiled, leaving 100 − 20 = 80 kg of saleable rice.

3. To earn a 25% profit on the cost, the total revenue required = Cost Price + Profit = 250 + (25% of 250) = 250 + 62.5 = Rs. 312.50.

4. This entire Rs. 312.50 must come from selling only the 80 kg of remaining rice.

5. To express this as a rate “per quintal” (i.e., per 100 kg) of the original purchase, scale up: Selling price per quintal = 312.5 × (100/80) = Rs. 390.625.

Cross-check

Check: selling the 80 kg of surviving rice at Rs. 390.625 per quintal gives revenue = 390.625 × (80/100) = Rs. 312.50, which equals the cost (Rs. 250) plus the required profit (Rs. 62.50) — confirming the rate is consistent.