Adding water to milk for profit — Aptitude Question
Adding water to milk for profit: In what ratio must water be mixed with milk costing ₹32 per litre so that the… Answer and worked solution on CodeKairo.
- Topic: Mixtures & Alligation
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 120 seconds
Question
In what ratio must water be mixed with milk costing ₹32 per litre so that the seller gains 25% by selling the mixture at ₹32 per litre?
Options
- 1 : 3
- 1 : 4
- 1 : 5
- 2 : 5
Show the answer and the worked solution
Correct answer: B. 1 : 4
Worked solution
- To gain 25% selling at ₹32, the mixture must cost 32 ÷ 1.25 = ₹25.60 per litre.
- Alligation between water (₹0) and milk (₹32) at a mean of ₹25.60: water : milk = (32 − 25.6) : (25.6 − 0) = 6.4 : 25.6 = 1 : 4.
Answer: 1 : 4.
The idea
Convert the profit requirement into the cost the mixture must have, then treat water as a free ingredient in an ordinary alligation.
Shortcut. Selling at milk's own cost price, the whole gain comes from free water, so the water must be 25% of the milk bought: 1 : 4.
Common trap. 1 : 3 — making water 25% of the mixture rather than 25% of the milk; 1 : 3 gives a 33⅓% gain.