Profit and Loss — A man sells 16 mangoes for the cost price of 20 mangoes. What is his percentage gain?

Introduction / Context:
When a seller’s revenue for a smaller count equals the cost for a larger count, the per-unit selling price must be higher than the per-unit cost. The ratio directly yields the profit percentage on cost.

Given Data / Assumptions:

• Revenue from selling 16 units equals cost of 20 units.
• Uniform cost per unit.

Concept / Approach:
Let CP per mango = c. Then cost of 20 mangoes = 20c. If selling 16 mangoes fetches 20c, then SP per mango = (20c)/16 = 1.25c, i.e., 25% above cost. Profit% on cost is (SP − CP)/CP * 100 = (1.25c − c)/c * 100 = 25%.

Step-by-Step Solution:

Verification / Alternative check:
Use concrete numbers: If c = ₹ 4, cost(20) = ₹ 80. Selling 16 at SP_unit = ₹ 5 gives revenue ₹ 80. Profit per unit = ₹ 1 on a base of ₹ 4 ⇒ 25%.

Why Other Options Are Wrong:
18%, 20%, 16%, and 12.5% do not match the exact 1.25 ratio derived from 20/16.

Common Pitfalls:
Subtracting 20 − 16 = 4 and calling it 4% without relating it to the cost base; percent must be ratio-based, not difference-based.

Final Answer:
25%