Single correct option
The price of sugar rises by 25%. By what percentage must a household reduce its sugar consumption so that its expenditure on sugar rises by only 10%?
- A. 15%
- B. 20%
- C. 12%
- D. 10%
Show answer and solution
Answer: (C) 12%
Expenditure = Price × Consumption.
New expenditure factor = 1.10, new price factor = 1.25, so the consumption factor = 1.10 ÷ 1.25 = 0.88.
Consumption must fall by 1 − 0.88 = 12%.
Why others fail: 15% is 25 − 10 (subtracting percentages, invalid for products); 20% is the reduction needed to keep expenditure unchanged (1 ÷ 1.25 = 0.8); 10% is a guess.
Tip: For a product of two quantities, work with multiplying factors, never by adding or subtracting percentages.
New expenditure factor = 1.10, new price factor = 1.25, so the consumption factor = 1.10 ÷ 1.25 = 0.88.
Consumption must fall by 1 − 0.88 = 12%.
Why others fail: 15% is 25 − 10 (subtracting percentages, invalid for products); 20% is the reduction needed to keep expenditure unchanged (1 ÷ 1.25 = 0.8); 10% is a guess.
Tip: For a product of two quantities, work with multiplying factors, never by adding or subtracting percentages.
Saved on this device. Sign in or create a free account to keep it on every device.