In what ratio should teas costing Rs. 60/kg and Rs. 65/kg be mixed so that selling the mixture at Rs. 68.20/kg yields a 10% gain?

Problem restatementTwo teas are priced at Rs. 60 and Rs. 65 per kg. The mixture is sold at Rs. 68.20/kg for a 10% profit. Find the ratio of quantities (Rs. 60 : Rs. 65).

Given data

• SP (mixture) = 68.20
• Profit% = 10% ⇒ Mixture CP = 68.20 / 1.10 = 62
• H = 65, L = 60, M = 62

Concept/ApproachBy alligation, quantities of cheaper:dearer = (H − M) : (M − L).

Step-by-step calculationCheaper : Dearer = (65 − 62) : (62 − 60)= 3 : 2 ⇒ 3 : 2 (Rs. 60 : Rs. 65)

Common pitfallsApplying alligation directly to SP without first converting to CP, which would give a wrong mean price.

Final Answer3 : 2 (Rs. 60 : Rs. 65)