Mixing rice of two prices — Aptitude Question
Mixing rice of two prices: Rice at ₹40/kg is mixed with rice at ₹60/kg so that the mixture costs ₹52/kg. Answer and worked solution on CodeKairo.
- Topic: Mixtures & Alligation
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 45 seconds
Question
Rice at ₹40/kg is mixed with rice at ₹60/kg so that the mixture costs ₹52/kg. In what ratio are they mixed?
Options
- 3 : 4
- 2 : 3
- 3 : 2
- 1 : 2
Show the answer and the worked solution
Correct answer: B. 2 : 3
Worked solution
- Cheaper : dearer = (60 − 52) : (52 − 40) = 8 : 12 = 2 : 3.
- Check: (2 × 40 + 3 × 60)/5 = 260/5 = 52. ✓
Answer: 2 : 3.
The idea
The alligation cross: quantity of cheaper ÷ quantity of dearer = (dearer − mean) ÷ (mean − cheaper). The mean sits closer to the ingredient there is more of.
Shortcut. 52 sits 12/20 = 3/5 of the way from 40 to 60, so the dearer rice makes up 3/5 of the mix: cheaper : dearer = 2 : 3.
Common trap. 3 : 2 — setting the gaps the wrong way round (12 : 8); the cheaper rice takes the dearer price's gap, 60 − 52 = 8.