The price of diesel increases from Rs 45 per litre to Rs 50 per litre. A person wants his total expenditure on diesel to increase by only 5%. By what percentage should he reduce his consumption of diesel?

Introduction / Context:
This question is about the relationship between price, quantity and total expenditure. When the price per unit increases, a consumer may reduce the quantity consumed to keep total spending under control. The problem asks for the required percentage reduction in consumption so that the total expenditure increases by only a limited percentage, even though the price has gone up more sharply.

Given Data / Assumptions:

• Initial price of diesel = Rs 45 per litre.
• New price of diesel = Rs 50 per litre.
• Allowed increase in total expenditure = 5%.
• We need the percentage reduction in quantity consumed.
• Initial quantity is assumed to be q litres, and new quantity is q prime litres.

Concept / Approach:
Total expenditure E equals price per litre multiplied by quantity consumed. Let initial expenditure be E1 and new expenditure be E2. We have E1 = 45 * q. After the price increase, E2 = 50 * q prime, and it is given that E2 = 1.05 * E1 (since expenditure should increase by only 5%). From this equation we find the ratio q prime / q and then compute the percentage reduction in quantity as (1 - q prime / q) * 100%.

Step-by-Step Solution:
Step 1: Initial expenditure E1 = 45 * q. Step 2: New expenditure E2 = 50 * q prime. Step 3: We require E2 = 1.05 * E1 (5% increase in expenditure). Step 4: So, 50 * q prime = 1.05 * (45 * q) = 47.25 * q. Step 5: Therefore, q prime / q = 47.25 / 50. Step 6: Compute q prime / q = 0.945. Step 7: So the new quantity is 94.5% of the old quantity. Step 8: Percentage reduction in consumption = (1 - 0.945) * 100% = 0.055 * 100% = 5.5%.

Verification / Alternative check:
Assume an initial quantity, for example q = 100 litres. Initial expenditure = 45 * 100 = Rs 4500. New quantity after 5.5% reduction = 100 - 5.5 = 94.5 litres. New expenditure = 50 * 94.5 = Rs 4725. The percentage increase in expenditure = (4725 - 4500) / 4500 * 100% = 5%. This confirms that a 5.5% reduction in quantity works correctly.

Why Other Options Are Wrong:

• 5: This would lead to a slightly higher increase in expenditure than 5% because the reduction in quantity would be too small.
• 4: This reduction does not offset the price increase sufficiently.
• 4.5: This also underestimates the necessary reduction and leads to more than a 5% increase in spending.
• 6: This overcompensates and leads to less than the allowed 5% increase in expenditure.

Common Pitfalls:
A common mistake is to think that if price increases by a certain percentage, the quantity must reduce by the same percentage, which is incorrect. Others directly subtract percentages without forming the relationship between the products price * quantity. Always set up the equation for total expenditure before and after the change, and solve for the new quantity ratio carefully.

Final Answer:
The person should reduce his diesel consumption by 5.5% to limit the expenditure increase to 5%.