Discussion
In what ratio must rice at ₹30 per kg be mixed with rice at ₹45 per kg so that the mixture is worth ₹36 per kg?
Answer: C
Correct answer: 3 : 2
By the rule of alligation, the two quantities are in the inverse ratio of their distances from the mean price: \[ \frac{\text{cheaper quantity}}{\text{dearer quantity}} = \frac{\text{dearer price} - \text{mean}}{\text{mean} - \text{cheaper price}}. \] Here \[ \frac{45 - 36}{36 - 30} = \frac{9}{6} = \frac{3}{2}. \] So the ratio is 3 : 2 - three parts of the cheaper rice to two of the dearer. The result is worth checking directly: 3 kg at 30 and 2 kg at 45 cost \( 90 + 90 = 180 \) for 5 kg, which is 36 per kg as required. The mean must lie between the two prices for the problem to have a solution, and the larger share always goes to the ingredient whose price is nearer the mean - here the cheaper, since 36 is closer to 30 than to 45. That observation alone rules out 2 : 3 without any arithmetic.
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