Keeping the sugar bill the same — Aptitude Question
Keeping the sugar bill the same: The price of sugar rises by 25%. By what percent must a family cut its consumption… Answer and worked solution on CodeKairo.
- Topic: Percentages
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
The price of sugar rises by 25%. By what percent must a family cut its consumption so that its expenditure on sugar stays the same?
Options
- 20%
- 25%
- 30%
- 40%
Show the answer and the worked solution
Correct answer: A. 20%
Worked solution
- Let the old price be 100 and old consumption 100, so expenditure = 10,000.
- New price 125; for the same 10,000, consumption must be 10,000 ÷ 125 = 80.
- Cut = 100 − 80 = 20%.
Answer: 20%.
The idea
For a price rise of r%, the consumption cut that keeps spending fixed is 100r/(100 + r) percent. For a price fall of r%, the allowed rise is 100r/(100 − r) percent.
Shortcut. Spending fixed means price × consumption is constant: price × 5/4, so consumption × 4/5 — a cut of 1/5 = 20%.
Common trap. 25% — matching the price rise; a 25% cut with a 25% rise leaves spending at 1.25 × 0.75 = 93.75% of the old amount.