Draw off and replace — Aptitude Question
Draw off and replace: A vessel holds 20 litres of a mixture with milk and water in the ratio 3 : 1. Answer and worked solution on CodeKairo.
- Topic: Mixtures & Alligation
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 120 seconds
Question
A vessel holds 20 litres of a mixture with milk and water in the ratio 3 : 1. 4 litres is drawn off and replaced with water. What is the new ratio?
Options
- 2 : 1
- 3 : 2
- 11 : 9
- 12 : 8
Show the answer and the worked solution
Correct answer: B. 3 : 2
Worked solution
- Milk = 15 L, water = 5 L.
- The 4 L drawn off contains 3 L milk and 1 L water, leaving 12 L milk and 4 L water.
- Adding 4 L water gives 12 L milk and 8 L water.
- New ratio = 12 : 8 = 3 : 2.
Answer: 3 : 2.
The idea
What is drawn off has the same composition as the mixture, so remove both components proportionally. Only then add the replacement.
Shortcut. Only the milk falls: removing 4 of 20 litres keeps 4/5 of it, 15 → 12 L; the vessel is back to 20 L, so water is 8 L and the ratio 3 : 2.
Common trap. "11 : 9" — treating the 4 L drawn off as pure milk (15 − 4 = 11, 5 + 4 = 9) instead of mixture holding 1 L of water.