Ratio and Proportion

Concept:Alligation rule: The ratio of two ingredients is (dearer price – mean price) : (mean price – cheaper price).Explanation:First, find the cost price of the mixture.Selling price is $\text{₹}17.6$ and profit is $14.6\%$ of the selling price.Profit amount = $0.146 \times 17.6 = 2.5696$.Hence cost price = $17.6 - 2.5696 = 15.0304$.Let cheaper rice cost $\text{Rs.}13.84$ and dearer rice cost $\text{Rs}15.54$.The mean price (cost of mixture) is $\text{Rs. }15.0304$.Apply alligation: difference dearer – mean = $15.54 - 15.0304 = 0.5096$, mean – cheaper = $15.0304 - 13.84 = 1.1904$.Thus ratio (cheaper : dearer) = $0.5096 : 1.1904$.Simplify: $0.5096 / 1.1904 \approx 0.4286 = 3/7$, so the ratio is $3:7$.Verification: In $3:7$ proportion, for 10 units the total cost = $3 \times 13.84 + 7 \times 15.54 = 150.3$, average = $150.3 / 10 = 15.03$, which matches the cost price $\text{₹}15.0304$ within rounding.Answer:The two types of rice are mixed in the ratio $3:7$.