Working back through two changes — Aptitude Question
Working back through two changes: A number is increased by 20% and then decreased by 20%, giving 9,600. Answer and worked solution on CodeKairo.
- Topic: Percentages
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
A number is increased by 20% and then decreased by 20%, giving 9,600. What was the original number?
Options
- 9,216
- 9,800
- 10,000
- 10,400
Show the answer and the worked solution
Correct answer: C. 10,000
Worked solution
- Net factor = 1.2 × 0.8 = 0.96.
- 0.96 × original = 9,600, so original = 9,600 ÷ 0.96 = 10,000.
- Check: 10,000 → 12,000 → 9,600. ✓
Answer: 10,000.
The idea
Collapse the chain of changes into one multiplier, then divide the final value by it. Reversing the steps one at a time works too but invites sign errors.
Shortcut. The net effect is a 4% loss, so the original must exceed 9,600, and 4% of 10,000 is exactly 400 (10,000 − 400 = 9,600).
Common trap. "9,216" — applying the 0.96 factor to 9,600 a second time (multiplying) instead of dividing by it.