A person bought a used bike for ₹18,000, spent ₹2,000 on repairs, and sold it…

Concept — Profit percentage is always measured on the total cost price: every rupee spent to acquire the article and put it in saleable condition, which includes overheads such as repairs, transport or taxes, and not the purchase price alone. Formally, Profit % = (Selling Price − Total Cost Price) ÷ Total Cost Price × 100. So in any transaction that carries an overhead, the overhead must be folded into the cost base before any percentage is taken.

Applying it to this transaction —

1. Total cost price = ₹18,000 (purchase) + ₹2,000 (repairs) = ₹20,000.

2. Selling price = ₹23,000.

3. Profit = ₹23,000 − ₹20,000 = ₹3,000.

4. Profit % = (3,000 ÷ 20,000) × 100 = 15%.

Cross-check — Working backwards, 15% of ₹20,000 is ₹3,000, so the selling price would be ₹20,000 + ₹3,000 = ₹23,000, which matches the figure given in the question.

Where the cost base goes wrong —

• Measuring the same ₹3,000 gain against only the ₹18,000 purchase price gives about 16.67%, because it ignores the repair spend that was equally part of the cost.

• Treating the ₹2,000 repair spend itself as the gain gives 10%, which confuses an expense with a profit.

• Measuring the ₹3,000 gain against the ₹23,000 selling price gives about 13.04%, because the base for profit percentage is cost, never selling price.

The profit on the whole transaction is therefore 15%.