Keeping the bill unchanged — Percentages Aptitude Question
Keeping the bill unchanged: The price of sugar rises by 25%. By what percent must a family reduce 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 reduce its consumption so that its expenditure on sugar is unchanged?
Options
- 16⅔%
- 20%
- 25%
- 30%
Show the answer and the worked solution
Correct answer: B. 20%
Worked solution
- Take price 100 and consumption 100, so expenditure = 10,000.
- New price = 125, so consumption must be 10,000 ÷ 125 = 80.
- Reduction = 20 out of 100 = 20%.
Answer: 20%.
The idea
For a price rise of r%, the consumption cut that keeps spending level is 100r/(100 + r) percent. For a price fall it is 100r/(100 − r) percent more consumption.
Shortcut. Price up by 1/4 → consumption down by 1/(4 + 1) = 1/5 = 20%, since 5/4 × 4/5 = 1 keeps price × quantity fixed.
Common trap. 25% — cutting consumption by the same 25% the price rose, which leaves spending at 125 × 75 = 9,375, below the original 10,000.