Question

The price of sugar rises by 25%. By what percentage must a family reduce its consumption so that its expenditure on sugar stays the same?

• A. 16.67%
• B. 20%
• C. 25%
• D. 22.5%

Hint:

Try assuming a simple round number for the original price and quantity, then see what new quantity keeps the expenditure unchanged.

Answer 1

The Correct Option is B

Step 1: Assume convenient numbers: let the original price be Rs. 1 per kg and the original consumption be 100 kg, so the original expenditure $=100\times1=$ Rs. 100.
Step 2: After a 25% rise, the new price $=$ Rs. 1.25 per kg.
Step 3: For expenditure to remain Rs. 100 at the new price, the new consumption $=\dfrac{100}{1.25}=80$ kg.
Step 4: Reduction in consumption $=100-80=20$ kg, which is $\dfrac{20}{100}\times100\%=20\%$ of the original consumption.
\[\boxed{20\%}\]