If the price of kerosene is increased by 11 percent, by what percentage should a householder reduce consumption so that the total expenditure on kerosene remains unchanged?

Introduction / Context:
This question is a typical price and consumption adjustment problem. It tests understanding of inverse proportion: when price rises, consumption must fall for expenditure to remain constant. The relationship is slightly more subtle because the required reduction is not equal to the price increase percentage.

Given Data / Assumptions:

• Price of kerosene increases by 11 percent.
• Total expenditure on kerosene must remain the same.
• We need the percentage reduction in consumption.

Concept / Approach:
Expenditure = price * quantity. If expenditure is constant, then new price * new quantity = old price * old quantity. Hence, when price increases by a factor, quantity must decrease by the reciprocal factor. We express both in terms of the original price and consumption and then solve for the required reduction percentage.

Step-by-Step Solution:
Let original price = P and original consumption = Q.Original expenditure = P * Q.New price after 11 percent increase = 1.11 * P.Let new consumption = q.Condition for same expenditure: 1.11 * P * q = P * Q.Cancel P from both sides to get 1.11 * q = Q.So q = Q / 1.11.Reduction in consumption = Q - q = Q - Q / 1.11 = Q * (1 - 1 / 1.11).Fractional reduction = (1.11 - 1) / 1.11 = 0.11 / 1.11 = 1 / 10.09 approximately.More exactly, 0.11 / 1.11 = 1 / 10.09 ≈ 0.099, or about 9.09 percent.

Verification / Alternative check:
Take original price = Rs. 100 per unit and quantity = 100 units, so expenditure = Rs. 10,000. New price = 111 per unit. If consumption is reduced by 9.09 percent, new quantity ≈ 90.91 units. New expenditure = 111 * 90.91 ≈ 10,000, confirming that 9.09 percent reduction keeps expenditure constant.

Why Other Options Are Wrong:
Reducing consumption by 11 percent would make the expenditure drop below the original value. Values like 11.09 percent or 8.25 percent do not satisfy the condition of equal expenditure when computed precisely.

Common Pitfalls:
Many candidates incorrectly subtract the same percentage as the price increase from consumption. Others forget that the base for the percentage reduction is the new consumption, not the original expenditure. Always set up the product price * quantity explicitly.

Final Answer:
The consumption of kerosene must be reduced by approximately 9.09 percent.