Three replacements — Mixtures & Alligation Aptitude Question
Three replacements: A cask holds 80 litres of wine. 8 litres is drawn off and replaced with water three times. Answer and worked solution on CodeKairo.
- Topic: Mixtures & Alligation
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
A cask holds 80 litres of wine. 8 litres is drawn off and replaced with water three times. How much wine is left?
Options
- 46.6 L
- 52.4 L
- 58.3 L
- 64.8 L
Show the answer and the worked solution
Correct answer: C. 58.3 L
Worked solution
- Fraction remaining each time = 1 − 8/80 = 0.9.
- After three operations: 80 × 0.729 = 58.32 ≈ 58.3 L.
Answer: 58.3 L.
The idea
The same power rule with n = 3. Note that the amount drawn each time is the same volume, not the same amount of wine.
Shortcut. Take 10% off three times: 80 → 72 → 64.8 → 58.32.
Common trap. 64.8 L — stopping one draw short (80 × 0.9² instead of 80 × 0.9³).