Question
A tea merchant has tea of two kinds, costing Rs 200 per kg and Rs 260 per kg. In what ratio should he mix them so that by selling the mixture at Rs 270 per kg, he gains 20%?
Solution
Let cost price of mixture = x per kg. He sells at 270 with 20% profit: 270 = x(1 + 20/100) = 1.2x x = 270 / 1.2 = 225 per kg So the mixture must cost Rs 225 per kg. Use alligation on costs 200 and 260 to get 225: Cheaper: 200 Dearer: 260 Mean: 225 Ratio (Cheaper : Dearer) = (260 − 225) : (225 − 200) = 35 : 25 = 7 : 5 So he should mix Rs 200 tea and Rs 260 tea in the ratio 7 : 5.
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