Mixing for a target selling price — Aptitude Question
Mixing for a target selling price: In what ratio must tea at ₹80 per kg be mixed with tea at ₹120 per kg so that… Answer and worked solution on CodeKairo.
- Topic: Mixtures & Alligation
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 105 seconds
Question
In what ratio must tea at ₹80 per kg be mixed with tea at ₹120 per kg so that selling the mixture at ₹110 per kg gives a 10% profit?
Options
- 1 : 1
- 1 : 2
- 1 : 3
- 3 : 1
Show the answer and the worked solution
Correct answer: A. 1 : 1
Worked solution
- Cost required = 110 ÷ 1.10 = ₹100 per kg.
- Alligation: (120 − 100) : (100 − 80) = 20 : 20 = 1 : 1.
- Checking against the options, the ratio is 1 : 1.
Answer: 1 : 1.
The idea
Convert the profit requirement into the mixture's cost first, then apply alligation to that cost as the mean.
Shortcut. ₹110 at a 10% profit is a cost of ₹100, the exact midpoint of ₹80 and ₹120, so the parts are equal: 1 : 1.
Common trap. "1 : 3" — alligating with the selling price ₹110 as the mean: (120 − 110) : (110 − 80) = 10 : 30.