Water added for a 20% gain — Aptitude Question
Water added for a 20% gain: A milkman mixes water with milk and sells the mixture at cost price, gaining 20%. Answer and worked solution on CodeKairo.
- Topic: Mixtures & Alligation
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
A milkman mixes water with milk and sells the mixture at cost price, gaining 20%. What is the ratio of water to milk?
Options
- 1 : 4
- 1 : 5
- 1 : 6
- 2 : 5
Show the answer and the worked solution
Correct answer: B. 1 : 5
Worked solution
- A 20% gain means the free water is one fifth of the milk bought.
- Taking 5 litres of milk and 1 litre of water gives a gain of 1/5 = 20%. ✓
- Water : milk = 1 : 5.
Answer: 1 : 5.
The idea
The gain equals water ÷ milk, because the water costs nothing and sells at the milk's price. Dividing by the mixture instead would give 16⅔%.
Shortcut. A 20% gain at cost price means 6 litres are sold for every 5 litres paid for, so 1 litre in every 6 is free water: water : milk = 1 : 5.
Common trap. "1 : 6" — comparing the water with the whole 6-litre mixture instead of with the 5 litres of milk.