Shilpi sold a washing machine for ₹ 10200. She incurred a loss of 15% in this…

Concept

When an item is sold at a loss, the loss percentage is always calculated on the cost price (CP), not the selling price (SP). The relation is SP = CP × (1 − Loss%/100), so given SP and the loss percentage, the cost price can be recovered as CP = SP ÷ (1 − Loss%/100).

Application

1. Let the cost price be CP. Given: selling price SP = ₹10200, loss = 15% of CP.

2. Since the loss is 15% of the cost price, the selling price equals 85% of the cost price: SP = CP × (1 − 15/100) = CP × 0.85.

3. Substitute the given selling price: 10200 = CP × 0.85.

4. Solve for CP: CP = 10200 ÷ 0.85 = ₹12000.

Cross-check

If CP = ₹12000, the loss amount is 12000 − 10200 = ₹1800, and the loss percentage is (1800 ÷ 12000) × 100 = 15%, which matches the loss percentage given in the question.

Hence, Shilpi bought the washing machine for ₹12000.