In what ratio must a grocer mix two varieties of rice costing ₹195 and ₹138…

Concept: Alligation is used to find the ratio in which two ingredients of different unit costs must be mixed to obtain a mixture of a specified mean cost. For a cheaper item priced a and a dearer item priced b mixed to get mean price m (where a < m < b), the rule of alligation gives Quantity(cheaper) : Quantity(dearer) = (b − m) : (m − a).

1. Identify the given costs and mean: dearer price b = ₹195, cheaper price a = ₹138, mean price m = ₹149 (since a < m < b, the standard alligation rule applies).

2. Apply the alligation rule: Quantity(cheaper) : Quantity(dearer) = (b − m) : (m − a) = (195 − 149) : (149 − 138) = 46 : 11.

3. The question asks for the ratio in the order costly-to-cheap (₹195 rice to ₹138 rice), so invert the ratio: Quantity(₹195 rice) : Quantity(₹138 rice) = 11 : 46.

Cross-check: verify by computing the mean cost of a mixture in ratio 11:46 — (195 × 11 + 138 × 46) / (11 + 46) = (2145 + 6348) / 57 = 8493 / 57 = ₹149, which matches the given mean price, confirming the ratio.

So the required ratio in which the grocer must mix the ₹195 and ₹138 rice is 11 : 46.