The price of onion rises from Rs. 24 per kg to Rs. 36 per kg. By what percentage should a household reduce consumption so that its expenditure on onions remains the same?

Introduction / Context:
This question deals with the relationship between price, quantity, and expenditure. When the price of a commodity increases, a consumer must either increase expenditure or reduce consumption to keep the total spending constant. Here, we want to maintain the same expenditure on onions even though the price per kilogram has increased, so we must find the required percentage reduction in quantity purchased.

Given Data / Assumptions:
Original price of onion = Rs. 24 per kg.
New price of onion = Rs. 36 per kg.
Total expenditure before and after the price rise should remain constant.
We must find the percentage decrease in consumption (quantity) of onions.

Concept / Approach:
Expenditure is given by price * quantity. Let the original quantity be Q kilograms. The original expenditure is 24 * Q. After the price rise, new price is 36 per kg. Let the new quantity be q kilograms. To keep expenditure the same, 24 * Q must equal 36 * q. From this equation, we can express q in terms of Q and find the ratio q / Q. Once we have the ratio of new quantity to old quantity, we can compute the percentage decrease in quantity as (Q - q) / Q * 100. Because price increased by a factor of 1.5 (from 24 to 36), quantity must adjust inversely by a factor of 2 / 3.

Step-by-Step Solution:
Let the original quantity purchased be Q kg. Original price per kg = Rs. 24, so original expenditure = 24 * Q. New price per kg = Rs. 36, let new quantity be q kg. Since expenditure is unchanged: 24 * Q = 36 * q. Solve for q: q = (24 / 36) * Q = (2 / 3) * Q. Thus, new quantity is two thirds of the original quantity. Decrease in quantity = Q - q = Q - (2 / 3) * Q = (1 / 3) * Q. Percentage decrease = (decrease / original quantity) * 100 = (1 / 3) * 100 = 33.33 percent (approximately).

Verification / Alternative check:
Assume a concrete original quantity, for example Q = 3 kg. Original expenditure = 24 * 3 = 72 rupees. After the price rise, the new price is 36 per kg. If the quantity is reduced to q = 2 kg (which is two thirds of 3), then new expenditure = 36 * 2 = 72 rupees, exactly the same as before. The reduction from 3 kg to 2 kg is 1 kg, which is 1 / 3 of 3 kg, that is 33.33 percent. This numerical example confirms our algebraic result.

Why Other Options Are Wrong:
A 25 percent reduction would make the new quantity 75 percent of the old one, which would not balance the 50 percent increase in price. A 50 percent reduction in quantity would lower expenditure far below the original, since price increased only by 50 percent. A 20 percent reduction is too small and would cause total expenditure to increase. Only a 33.33 percent reduction exactly offsets the price increase from 24 to 36 per kg.

Common Pitfalls:
Some learners try to subtract the percentages directly, which is not valid. Others incorrectly assume that a 50 percent increase in price demands a 50 percent decrease in quantity, not realizing the inverse proportionality in the expenditure formula. It is also easy to mix up the roles of price and quantity when setting up the equation. Always start from the equation price1 * quantity1 = price2 * quantity2 when expenditure must stay the same, then solve systematically for the unknown quantity and compute the required percentage change.

Final Answer:
The household should reduce its onion consumption by approximately 33.33 percent to keep expenditure the same.