Numerical answer
A shopkeeper mixes two varieties of rice costing ₹60/kg and ₹90/kg. He sells the mixture at ₹96/kg, making a 20% profit. If the cheaper variety is used in quantity a and the costlier in quantity b, find the value of b/a.
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Answer: 2
Cost price of the mixture = SP/1.20 = 96/1.2 = ₹80/kg. Using the mixture equation: 60a + 90b = 80(a+b) ⟹ 60a + 90b = 80a + 80b ⟹ 10b = 20a ⟹ b/a = 2. (By alligation, cheaper:costlier = (90−80):(80−60) = 10:20 = 1:2, confirming b/a = 2.)
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