Rice at two prices — Mixtures & Alligation Aptitude Question
Rice at two prices: Rice costing ₹50 per kg is mixed with rice costing ₹70 per kg to give a mixture worth ₹56 per kg. Answer and worked solution on CodeKairo.
- Topic: Mixtures & Alligation
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
Rice costing ₹50 per kg is mixed with rice costing ₹70 per kg to give a mixture worth ₹56 per kg. In what ratio?
Options
- 3 : 2
- 7 : 3
- 2 : 3
- 3 : 7
Show the answer and the worked solution
Correct answer: B. 7 : 3
Worked solution
- Cheaper : dearer = (70 − 56) : (56 − 50) = 14 : 6 = 7 : 3.
- Check: (7 × 50 + 3 × 70)/10 = 560/10 = 56. ✓
Answer: 7 : 3.
The idea
The mean at 56 is much nearer 50, so far more of the cheaper grade is needed. That sanity check catches an inverted ratio.
Shortcut. 56 is below the midpoint 60, so more of the cheaper rice is needed — 3 : 2 or 7 : 3; 3 : 2 gives (150 + 140) ÷ 5 = 58, so 7 : 3.
Common trap. "3 : 7" — pairing each price with its own distance from 56, (56 − 50) : (70 − 56), which inverts the alligation.