The price of petrol is increased by 20%. By what percent should the…

Concept: When Expenditure = Price × Consumption, keeping expenditure constant after a percentage increase in price requires a proportionally smaller percentage decrease in consumption. If price increases by r%, the required percentage reduction in consumption is (r / (100 + r)) × 100 — not simply r%, because the increase and the reduction are measured against different bases (new price vs. original consumption).

Application:

1. Assume the original price = 100 and original consumption = 100, so the original expenditure = 100 × 100 = 10,000.

2. After a 20% increase, the new price = 100 + 20 = 120.

3. Let the required percentage reduction in consumption be x. The new consumption = 100 − x.

4. For expenditure to stay the same: 120 × (100 − x) = 10,000.

5. Dividing both sides by 120: 100 − x = 10000/120 = 83.33.

6. So x = 100 − 83.33 = 16.67.

Cross-check: Using the direct formula, reduction % = (r / (100 + r)) × 100 = (20 / 120) × 100 = 16.67%, which matches the equation-based derivation.

So the consumption must be reduced by 16.67%.