The price of petrol increases from Rs 60 per litre to Rs 75 per litre. By what percentage should a household reduce its consumption of petrol so that its total expenditure on petrol increases by only 10%?

Introduction / Context:
This question involves a price increase for petrol and a controlled increase in expenditure. It tests the understanding of how changes in price and quantity interact. The key idea is that to limit the rise in spending, consumption must be reduced appropriately to offset part of the price increase.

Given Data / Assumptions:

• Original price of petrol = Rs 60 per litre.
• New price of petrol = Rs 75 per litre.
• Desired increase in total expenditure = 10 percent.
• Original consumption = q litres (unknown).
• New consumption after adjustment = q dash litres.
• We assume no other changes in conditions.

Concept / Approach:
Original expenditure is: E1 = 60 * q. New expenditure should be 10 percent more, so: E2 = 1.10 * E1 = 1.10 * 60 * q. At the new price of 75 per litre, the new expenditure is also: E2 = 75 * q dash. We equate these two expressions for E2 and solve for q dash in terms of q, then compute the percentage reduction in consumption: Reduction percent = ((q - q dash) / q) * 100.

Step-by-Step Solution:
Step 1: Original expenditure E1 = 60 * q. Step 2: New expenditure allowed, with 10 percent increase, E2 = 1.10 * 60 * q = 66 * q. Step 3: New expenditure at new price is also E2 = 75 * q dash. Step 4: Equate the two: 75 * q dash = 66 * q. Step 5: Solve for q dash: q dash = (66 / 75) * q. Step 6: Simplify 66 / 75 = 0.88, so q dash = 0.88 * q. Step 7: Reduction in consumption = q - q dash = q - 0.88q = 0.12q. Step 8: Reduction percent = (0.12q / q) * 100 = 12 percent.

Verification / Alternative check:
Assume an original consumption of 100 litres for simplicity. Original expenditure = 60 * 100 = Rs 6,000. Permitted new expenditure = 10 percent more = 6,000 * 1.10 = Rs 6,600. At Rs 75 per litre, new consumption = 6,600 / 75 = 88 litres. Reduction in consumption = 100 - 88 = 12 litres, which is 12 percent of 100. This numerical example confirms the theoretical result.

Why Other Options Are Wrong:
15 percent and 18 percent: These imply a larger reduction than needed, which would lead to an expenditure increase of less than 10 percent. 20 percent: This reduction is too high and would significantly underuse the allowed increased budget. 10 percent: This value is smaller than required and would cause the expenditure to rise by more than 10 percent after the price increase.

Common Pitfalls:
Candidates often incorrectly compute the percentage reduction by comparing price changes alone, ignoring the controlled expenditure increase. Some also mistakenly treat the change in price from 60 to 75 as 15 percent instead of 25 percent. The correct approach is to equate the target new expenditure with the product of new price and new quantity, then work out the ratio of new quantity to old quantity carefully.

Final Answer:
The household should reduce petrol consumption by 12 percent to limit the expenditure increase to 10 percent.