In what ratio must rice of Rs.16 per kg be mixed with rice of Rs.24 per kg so…

Concept: The rule of alligation gives the ratio in which a cheaper item (price C) and a dearer item (price D) must be mixed to obtain a mixture at a mean price M. That ratio, cheaper : dearer, equals (D − M) : (M − C).

Application:

1. Here the cheaper rice costs C = Rs.16/kg, the dearer rice costs D = Rs.24/kg, and the required mean price is M = Rs.18/kg.

2. Compute the two differences: D − M = 24 − 18 = 6, and M − C = 18 − 16 = 2.

3. By the alligation rule, cheaper : dearer = 6 : 2, which reduces to 3 : 1.

Cross-check: Take 3 parts of the Rs.16 rice and 1 part of the Rs.24 rice. Total cost = 3×16 + 1×24 = 48 + 24 = 72, over 4 parts, giving 72/4 = Rs.18 per kg — exactly the required mean price, so the ratio checks out.

So the rice must be mixed in the ratio 3:1.