A fraction after two changes — Percentages Aptitude Question
A fraction after two changes: If the numerator of a fraction is increased by 20% and the denominator decreased by… Answer and worked solution on CodeKairo.
- Topic: Percentages
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 105 seconds
Question
If the numerator of a fraction is increased by 20% and the denominator decreased by 10%, the new fraction is 20/21. What was the original fraction?
Options
- 3/5
- 5/7
- 5/8
- 7/9
Show the answer and the worked solution
Correct answer: B. 5/7
Worked solution
- (1.2n)/(0.9d) = 20/21.
- n/d = (20/21) × (0.9/1.2) = (20/21) × 0.75 = 15/21 = 5/7.
- Check: numerator 5 → 6, denominator 7 → 6.3, and 6/6.3 = 20/21. ✓
Answer: 5/7.
The idea
Apply the multipliers to numerator and denominator separately, then invert the whole relation to recover the original. Checking the answer forwards is quick and worth doing.
Shortcut. The changes multiply the fraction by 1.2/0.9 = 4/3. Test the options: 5/7 × 4/3 = 20/21, while 3/5, 5/8 and 7/9 give 4/5, 5/6 and 28/27.
Common trap. "7/9" — the option closest in size to 20/21, which looks right if the changes seem small; but they raise the fraction by a third, so the original must be near 0.71.