If the price of diesel increases by 25% and Karthik decides that his total spending on diesel can increase by only 15%, by what percentage must he reduce the quantity of diesel he purchases so that his expenditure remains within this new limit?

Introduction / Context:
In many aptitude and percentage based word problems, the price of a commodity changes and the buyer wants to control or limit the total spending. This question tests the important idea that expenditure is equal to price multiplied by quantity. When the price of diesel increases but Karthik allows his total diesel budget to increase only partly, he must adjust the quantity purchased. Understanding this relation is essential for solving a wide range of exam problems related to inflation, family budgets, and consumption changes.

Given Data / Assumptions:

• Initial diesel price is P per litre.
• Initial quantity bought is Q litres.
• Initial expenditure is P * Q.
• Price increases by 25%, so new price is 1.25 * P.
• Allowed increase in expenditure is 15%, so new expenditure is 1.15 * P * Q.
• New quantity purchased is q litres and Karthik wants the new expenditure to match his allowed limit.

Concept / Approach:
The key concept is that Expenditure = Price * Quantity. When price changes by a certain percentage and expenditure is allowed to change by another percentage, the required percentage change in quantity can be found by equating initial and new expenditure expressions. We find the new quantity as a multiplier of the old quantity, then convert the difference into a percentage reduction. This method avoids trial and error and works for all similar questions in competitive exams.

Step-by-Step Solution:
Let initial price be P and initial quantity be Q, so initial expenditure is P * Q.Price increases by 25%, so new price becomes 1.25 * P.Allowed expenditure increases by 15%, so new expenditure can be at most 1.15 * P * Q.Let new quantity be q, then new expenditure is 1.25 * P * q.Equate allowed new expenditure and actual new expenditure: 1.25 * P * q = 1.15 * P * Q.Cancel P on both sides to get 1.25 * q = 1.15 * Q, so q = (1.15 / 1.25) * Q = 0.92 * Q.Thus new quantity is 92% of old quantity, so reduction in quantity is 8% of Q.

Verification / Alternative check:
Assume a simple numerical example for confirmation. Let price initially be Rs 100 per unit and quantity be 1 unit. Initial expenditure is Rs 100. After a 25% increase, new price is Rs 125. If expenditure rises by only 15%, allowed new expenditure is Rs 115. The quantity that can now be bought is 115 / 125, which equals 0.92 units. This matches 92% of the original quantity, confirming that the reduction is 8%. The arithmetic therefore supports the algebraic derivation and confirms the final percentage reduction value.

Why Other Options Are Wrong:
Option 6.67% is wrong because it would result from incorrect handling of the ratio 1.15 to 1.25. The correct ratio is 0.92, not approximately 0.9333.

Option 7.41% is incorrect because it corresponds to a different pair of percentage changes and does not fit the numbers used in this problem.

Option 9% is too high, and if used it would give a smaller expenditure than allowed, which does not match the condition that Karthik spends exactly 15% more.

Common Pitfalls:
A common mistake is to subtract 15 from 25 and assume that quantity must reduce by 10%, which is wrong because expenditure depends on a product of price and quantity, and percentage changes in a product do not combine by simple subtraction. Another typical error is to treat 1.15 / 1.25 as 1.25 / 1.15. Careful attention to which quantity goes in the numerator is crucial. Students should also remember to express the final answer as the percentage reduction, that is the difference between original quantity and new quantity relative to the original quantity, not the remaining percentage of quantity.

Final Answer:
The required reduction in the quantity of diesel purchased is 8%.