Replacing milk with water, twice — Aptitude Question
Replacing milk with water, twice: A vessel holds 100 L of milk. 10 L is drawn off and replaced with water, and this… Answer and worked solution on CodeKairo.
- Topic: Mixtures & Alligation
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 50 seconds
Question
A vessel holds 100 L of milk. 10 L is drawn off and replaced with water, and this is done twice in all. How much milk remains?
Options
- 80 L
- 81 L
- 82 L
- 90 L
Show the answer and the worked solution
Correct answer: B. 81 L
Worked solution
- Each operation removes 10% of the current milk, leaving 90%.
- After two operations: 100 × 0.9² = 81 L.
Answer: 81 L.
The idea
Repeated replacement: remaining = initial × (1 − drawn/total)ⁿ. It is a compound-decay formula in disguise.
Shortcut. The first draw removes 10 L of milk, the second only 9 L (a tenth of 90), so 100 − 10 − 9 = 81 L.
Common trap. 80 L — taking 10 L of milk out each time; the second 10 L drawn is only 90% milk.