Blending two varieties of rice — Aptitude Question
Blending two varieties of rice: Rice at ₹30 per kg is mixed with rice at ₹45 per kg so that the mixture is worth… Answer and worked solution on CodeKairo.
- Topic: Mixtures & Alligation
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 50 seconds
Question
Rice at ₹30 per kg is mixed with rice at ₹45 per kg so that the mixture is worth ₹35 per kg. In what ratio are they mixed?
Options
- 1 : 2
- 2 : 1
- 2 : 3
- 3 : 2
Show the answer and the worked solution
Correct answer: B. 2 : 1
Worked solution
- Cheaper : dearer = (45 − 35) : (35 − 30) = 10 : 5 = 2 : 1.
- Check: (2 × 30 + 1 × 45)/3 = 105/3 = 35. ✓
Answer: 2 : 1.
The idea
The alligation cross gives quantity of cheaper ÷ quantity of dearer = (dearer − mean) ÷ (mean − cheaper). The mean sits nearer the ingredient there is more of.
Shortcut. ₹35 is a third of the way from ₹30 to ₹45, so the dearer rice is one part in three: 2 : 1.
Common trap. 1 : 2 — writing the distances 5 : 10 in the same order as the prices instead of crossing them; that mix would average ₹40.