If the price of petrol increases by 20%, by what percentage should consumption be reduced so that expenditure on petrol remains unchanged?

Introduction / Context: With expenditure E = price * quantity held constant, any increase in price must be offset by a proportional decrease in quantity. The relation is multiplicative, not additive.

Given Data / Assumptions:

• Price increases by 20% ⇒ price multiplier = 1.20.
• Expenditure must remain the same.

Concept / Approach: If original quantity is Q, new quantity Q′ must satisfy 1.20 * Q′ = Q, hence Q′ = Q / 1.20 = (5/6)Q. The reduction equals Q − Q′ = (1/6)Q, which as a percentage of Q is 16 2/3%.

Step-by-Step Solution:

Verification / Alternative check: Example: Original spend = ₹120 at ₹12/L gives 10 L. New price ₹14.40/L; buying 8.333… L costs ₹120 again. Reduction is 1.666… L on 10 L = 16 2/3%.

Why Other Options Are Wrong: 20% assumes additive logic; 15% or 8% under-adjust; 6 2/3% divides by the wrong base.

Common Pitfalls: Adding −20% directly to quantity change instead of using the inverse multiplier.

Final Answer: 16 2/3%