A man sells 320 mangoes at the cost price of 400 mangoes. His gain percent is

Concept: When a trader sells fewer articles (say a) at the price that would normally be charged for a larger number of articles (say b, with b greater than a) — that is, the selling price of a articles equals the cost price of b articles — the resulting gain percent follows the identity Gain% = [(b − a) / a] × 100. This holds because the actual cost of the a articles sold is smaller than the cost of b articles, so the cost-value of the extra (b − a) articles becomes the gain earned on the a articles that were actually sold.

1. Let the cost price of one mango be Rs 1 (a convenient unit, since only the percentage is required).

2. Cost price of 400 mangoes = 400 × Rs 1 = Rs 400.

3. The statement says the man sells 320 mangoes at the cost price of 400 mangoes, so Selling Price of 320 mangoes = Rs 400.

4. Cost Price of the 320 mangoes actually sold = 320 × Rs 1 = Rs 320.

5. Gain = Selling Price − Cost Price = Rs 400 − Rs 320 = Rs 80.

6. Gain% = (Gain / Cost Price) × 100 = (80 / 320) × 100 = 25%.

Cross-check: Apply the identity directly with a = 320 and b = 400: Gain% = [(400 − 320) / 320] × 100 = (80 / 320) × 100 = 25%, which matches the step-by-step working above.