Working back to the price rise — Aptitude Question
Working back to the price rise: When the price of a commodity rose, a family reduced its consumption by 20% and its… Answer and worked solution on CodeKairo.
- Topic: Percentages
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
When the price of a commodity rose, a family reduced its consumption by 20% and its expenditure stayed the same. By what percent did the price rise?
Options
- 20%
- 25%
- 30%
- 33⅓%
Show the answer and the worked solution
Correct answer: B. 25%
Worked solution
- Let the old price be p and consumption 100, so expenditure = 100p.
- New consumption = 80, so the new price q satisfies 80q = 100p → q = 1.25p.
- The price rose by 25%.
Answer: 25%.
The idea
This is the previous question read backwards. Fixing the product price × quantity and solving for the missing factor handles both directions.
Shortcut. Consumption down by 1/5 → price up by 1/(5 − 1) = 1/4 = 25%, since 4/5 × 5/4 = 1.
Common trap. 20% — assuming the price rose by the same 20% that consumption fell.