If the price of sugar increases from Rs. 6 per kilogram to Rs. 7.50 per kilogram, by what percentage should a person reduce consumption of sugar so that there is no increase in total expenditure on sugar?

Introduction:
This question is a classic example from the topic of percentage change and consumption. It tests the concept that when price changes but expenditure is kept constant, the quantity consumed must adjust inversely in order to maintain the same expenditure level.

Given Data / Assumptions:
Original price of sugar = Rs. 6 per kilogram.
New price of sugar = Rs. 7.50 per kilogram.
Total expenditure on sugar is to remain unchanged.
We are asked to find the percentage reduction in consumption (quantity) of sugar.

Concept / Approach:
Expenditure is given by price * quantity. If total expenditure remains constant and price increases, then quantity must decrease in such a way that price * quantity stays the same. The relationship between the original and new quantities under constant expenditure is inverse proportionality. Therefore we can find the ratio of the new quantity to the old quantity as old price / new price, and then convert the drop in quantity into a percentage decrease.

Step-by-Step Solution:
Let the original quantity of sugar purchased be Q kilograms. Original expenditure = 6 * Q. Let the new quantity after price increase be Q2 kilograms. New price per kilogram is Rs. 7.50. Expenditure remains constant, so 6 * Q = 7.50 * Q2. Solve for Q2: Q2 = (6 * Q) / 7.50. Compute 6 / 7.50 = 0.8. So Q2 = 0.8 * Q. This means the new quantity is 80% of the old quantity. Percentage decrease in quantity = (Q - Q2) / Q * 100. Substitute Q2 = 0.8 * Q: (Q - 0.8 * Q) / Q * 100 = 0.2 * 100 = 20%.
Verification / Alternative check:
Assume a numerical example. Suppose initially the person buys 10 kilograms. Expenditure at Rs. 6 per kilogram is 10 * 6 = Rs. 60. After the price increase to Rs. 7.50, to keep spending at Rs. 60, the person can buy 60 / 7.50 = 8 kilograms. The quantity has decreased from 10 kilograms to 8 kilograms, a drop of 2 kilograms. The percentage decrease is 2 / 10 * 100 = 20%. This confirms the algebraic result.

Why Other Options Are Wrong:
A 15% reduction would leave quantity at 85% of the original, 25% would leave 75%, and so on. None of these would satisfy the constant expenditure condition when combined with the new price of Rs. 7.50. Only a 20% reduction produces a new quantity that leads to equal expenditure before and after the price rise.

Common Pitfalls:
Some students mistakenly compute the percentage increase in price and then assume the same percentage decrease is required in quantity, which is not correct. The connection between price and quantity under constant expenditure is inverse, not symmetric in percentage terms. Another common error is to subtract Rs. 6 from Rs. 7.50 and then misinterpret this difference directly as a percentage reduction needed in quantity.

Final Answer:
The person must reduce sugar consumption by 20% to keep expenditure the same.