Two replacements from a ratio — Aptitude Question
Two replacements from a ratio: A cask holds 64 litres of milk. 8 litres is removed and replaced with water, twice. Answer and worked solution on CodeKairo.
- Topic: Mixtures & Alligation
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
A cask holds 64 litres of milk. 8 litres is removed and replaced with water, twice. How much milk remains?
Options
- 48 L
- 49 L
- 50 L
- 56 L
Show the answer and the worked solution
Correct answer: B. 49 L
Worked solution
- Fraction remaining each time = 1 − 8/64 = 7/8.
- After two operations: 64 × (7/8)² = 64 × 49/64 = 49 L.
Answer: 49 L.
The idea
The power rule again. Choosing numbers where the fraction cancels against the volume makes the arithmetic exact.
Shortcut. Each draw takes an eighth of the milk present: 64 → 56 (8 L out) → 49 (7 L out).
Common trap. "48 L" — subtracting 8 L of milk both times; the second draw is mixture and carries only 7 L of milk.