Price–consumption adjustment: If the price of petrol rises by 20%, by what percentage must consumption be reduced so that total expenditure on petrol remains unchanged?

Introduction / Context:A classic inverse-percentage problem: when price goes up, to keep spending the same, consumption must drop in the exact inverse proportion.

Given Data / Assumptions:

• Price increase r = 20%.
• Expenditure = Price * Quantity is to remain constant.
• We seek percentage decrease in quantity.

Concept / Approach:When price increases by r%, quantity must be multiplied by 1/(1 + r). The percentage decrease needed is r/(100 + r) * 100%.

Step-by-Step Solution:

Verification / Alternative check:Assume initial price = 100 and quantity = 1 (expenditure = 100). New price = 120. To keep expenditure 100, quantity = 100/120 = 5/6, i.e., a reduction of 1/6 = 16 2/3%.

Why Other Options Are Wrong:

• 6 2/3%, 8%, 15%, 12.5% do not satisfy constant-expenditure arithmetic with a 20% price rise.

Common Pitfalls:Subtracting 20% directly from quantity instead of using the inverse formula; that would under-compensate.

Final Answer:16 2/3%