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Three types of grain costing ₹50/kg, ₹70/kg, and an unknown price are mixed in the ratio 2:3:2. If the mixture is sold at ₹64/kg with 20% profit, what is the price of the third variety?

1. ₹ 31.6/kg
2. ₹ 32.8/kg
3. ₹ 24.2/kg
4. ₹ 36/kg

Correct answer: ₹ 31.6/kg

Solution

Selling price is ₹64/kg with 20% profit, so cost price of the mixture is ₹64 ÷ 1.2 = ₹53.33/kg. Using the weighted average, (2×50 + 3×70 + 2×x)/7 = 53.33, which gives x = ₹31.6/kg.

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