Ratio and Proportion

Concept:The cost price of the mixture is found from the selling price and profit percentage on sale price, then the mixing ratio is obtained by alligation.Explanation:Selling price of the mixture = $\text{Rs.}8.80$ per kg.Profit = $17.5\%$ of selling price = $0.175 \times 8.80 = 1.54$.So, cost price = $8.80 - 1.54 = \text{Rs.}7.26$ per kg.Let the cheaper tea (₹6.92) and dearer tea (₹7.77) be mixed in the ratio $x : y$.Using alligation:Difference of cheaper from mean = $7.26 - 6.92 = 0.34$.Difference of dearer from mean = $7.77 - 7.26 = 0.51$.Thus ratio $x : y = 0.51 : 0.34 = 51 : 34 = 3 : 2$.Answer:The required proportion is $3 : 2$.