The price of pulses increases by 25%; by what percentage should a family reduce its consumption of pulses so that its total expenditure on pulses remains unchanged?

Introduction / Context:
This question is another example of how price and quantity interact to determine expenditure. When the price of a commodity rises, a family that wants to keep expenditure unchanged must reduce quantity consumed in a specific proportion. Here the price of pulses has increased by 25% and we must calculate the required percentage reduction in consumption to keep the overall spending constant.

Given Data / Assumptions:

• Let the original price of pulses be P per unit.
• Let the original quantity consumed be Q units.
• Original expenditure is P * Q.
• Price increases by 25%, so new price is 1.25 * P.
• The family wants the expenditure on pulses to remain the same as before.
• Let the new quantity consumed be q units.

Concept / Approach:
The fundamental relation is Expenditure = Price * Quantity. If the price increases and expenditure stays constant, quantity must decrease accordingly. We express both original and new expenditure in terms of P, Q and q, then equate them. Solving for q in terms of Q gives the factor by which quantity must be adjusted. The percentage reduction in consumption is then found by comparing Q and q.

Step-by-Step Solution:
Original expenditure = P * Q.After price increase, new price = 1.25 * P.Let new quantity be q, so new expenditure = 1.25 * P * q.Since expenditure is to remain the same, we set 1.25 * P * q = P * Q.Cancel P from both sides to get 1.25 * q = Q.So q = Q / 1.25.Write 1.25 as 5 / 4, hence q = Q * (4 / 5) = 0.8 * Q.This means new quantity is 80% of the original quantity.Therefore, percentage reduction in consumption = 100% - 80% = 20%.

Verification / Alternative check:
Take a simple example. Suppose original price P is Rs. 100 per unit and quantity consumed Q is 1 unit. Expenditure is Rs. 100. After a 25% price increase, new price becomes 125 per unit. To keep expenditure at Rs. 100, the family can now buy q = 100 / 125 = 0.8 units. This is exactly 80% of the original quantity, indicating a 20% reduction. This consistent result confirms the algebraic solution and the final percentage reduction.

Why Other Options Are Wrong:
16% and 72% are unrelated to the actual ratio required to offset a 25% price increase while keeping expenditure constant.

84% would mean the family almost stops consuming pulses, which clearly does not correspond to just a 25% increase in price with unchanged expenditure.

Common Pitfalls:
Many students mistakenly think that a 25% increase in price means a 25% decrease in consumption to keep expenditure fixed, but this is incorrect because the product of price and quantity must remain the same. Others incorrectly compute the new quantity factor as 1 / (1 + 0.25) and then fail to convert it properly into a percentage reduction. Always set up the equation with original and new expenditures equal and carefully solve for the new quantity before converting to a percent change.

Final Answer:
The family must reduce its consumption of pulses by 20% to keep expenditure unchanged.