A man gains 20% by selling an article for a certain price. If he sells it at…

Concept: Profit percentage compares the profit earned to the original cost price: Profit% = ((Selling Price − Cost Price) / Cost Price) × 100. When the selling price is later changed, the cost price used in this formula never changes — only the selling price is scaled.

1. Let the cost price (CP) of the article be x.

2. A 20% gain means the first selling price (SP₁) = 120% of CP = (6/5)x.

3. The new selling price (SP₂) is double SP₁, so SP₂ = 2 × (6/5)x = (12/5)x.

4. New profit = SP₂ − CP = (12/5)x − x = (7/5)x.

5. New profit% = (Profit / CP) × 100 = [(7/5)x / x] × 100 = 140%.

Check: Take CP = 100: SP₁ = 120 (20% gain), SP₂ = 240 (double of 120), profit = 240 − 100 = 140, profit% = 140% — confirming the result independent of the algebraic variable.