In what ratio should rice costing ₹40 per kg be mixed with rice costing ₹55 per kg to get a mixture worth ₹45 per kg?
2 : 1. By alligation, cheaper : dearer = (55 - 45) : (45 - 40) = 10 : 5 = 2 : 1. Check: 2 kg at ₹40 plus 1 kg at ₹55 costs ₹135 for 3 kg, which is ₹45 per kg.
Explain it simply
The mean price sits between the two prices. The closer it sits to one of them, the more of that one you need. ₹45 is just ₹5 above the cheap rice but ₹10 below the costly rice, so you need twice as much cheap rice. Alligation is a quick way to write this "cross difference" rule.
Example
Question: Mix rice at ₹40/kg and ₹55/kg to get ₹45/kg. Find the ratio.
40 55
45
(55-45) (45-40)
10 : 5- Cheaper quantity : dearer quantity = 10 : 5 = 2 : 1.
- Check: 2 x 40 + 1 x 55 = 135 for 3 kg, so ₹45/kg.
Follow-up: to make 60 kg of the mixture, take 40 kg of the ₹40 rice and 20 kg of the ₹55 rice.
const cheap = 55 - 45, dear = 45 - 40;
console.log(cheap / dear); // Output: 2
console.log((2 * 40 + 1 * 55) / 3); // Output: 45What to say in the interview
"By alligation the ratio of cheaper to dearer is the dearer price minus the mean, to the mean minus the cheaper price. That's 10 to 5, or 2 to 1, and a quick cost check confirms ₹45 a kilo."
Common mistakes
- Writing the differences in the wrong order and getting 1 : 2.
- Using alligation when the mean is outside the two prices, which means the question has an error.