There was a hike in petrol price by 12%. By how much percentage should a person decrease his petrol consumption so that there is no change in his expenditure on petrol?

To maintain a constant expenditure when the price of a commodity increases, the consumption must decrease in an inverse proportion. Expenditure is defined as the product of price and quantity [2]. If the initial price is 100 and consumption is 100, the total expenditure is 10,000. A 12% hike increases the price to 112. To keep the expenditure at 10,000, the new quantity (Q) is calculated as 112 * Q = 10,000, which gives Q ≈ 89.285. The percentage reduction in consumption is therefore 100 - 89.285 = 10.714%. This follows the economic principle that if the percentage decline in quantity offsets the percentage increase in price, expenditure remains unchanged [1]. Mathematically, the formula for the required reduction is (r / (100 + r)) * 100, where r is the percentage increase. Substituting 12 for r gives (12 / 112) * 100 ≈ 10.7%.

Sources

1. [2] Microeconomics (NCERT class XII 2025 ed.) > Chapter 2: Theory of Consumer Behaviour > 2.6.3 Elasticity and Expenditure > p. 31
2. [1] Microeconomics (NCERT class XII 2025 ed.) > Chapter 2: Theory of Consumer Behaviour > 2.6.3 Elasticity and Expenditure > p. 32