The price of sugar rises by 20%, but expenditure is kept constant. What is the ratio of the reduction in consumption to the original consumption?

Introduction / Context:
When expenditure (Price * Quantity) is held constant and price changes, quantity must adjust inversely. A 20% price increase means the buyer must reduce consumption so that total spend remains unchanged.

Given Data / Assumptions:

• Initial price = P, initial quantity = Q, expenditure = P * Q.
• New price = 1.2P (20% higher).
• Expenditure must remain P * Q.

Concept / Approach:
Let new quantity be Q′. With constant expenditure: 1.2P * Q′ = P * Q ⇒ Q′ = Q / 1.2 = (5/6)Q. Reduction = Q − Q′ = Q − (5/6)Q = (1/6)Q. Hence, reduction : original = (1/6)Q : Q = 1 : 6.

Step-by-Step Solution:

Verification / Alternative check:
Take P = 10, Q = 6 ⇒ spend = 60. New price = 12; to keep spend 60, Q′ = 5. Reduction 1 on original 6 ⇒ 1 : 6.

Why Other Options Are Wrong:
Ratios 1:3, 1:4, 1:5 correspond to price changes of 50%, 33 1/3%, and 25% respectively for constant spend, not 20%.

Common Pitfalls:
Subtracting 20 from 100 directly to claim a “20:100 = 1:5” ratio without using the inverse relationship required by constant expenditure.

Final Answer:
1 : 6