Chetan purchased 10 kg of rice at the rate of ₹38 per kg and 31 kg of rice at…
2025
Chetan purchased 10 kg of rice at the rate of ₹38 per kg and 31 kg of rice at ₹46 per kg. He sold the whole mixture at the rate of ₹44 per kg. Find his loss (in ₹).
- A.
10
- B.
7
- C.
2
- D.
5
Attempted by 3 students.
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Correct answer: C
When two lots of the same item bought at different rates are combined and sold together at one rate, the mixture's overall profit or loss is the difference between the total selling price and the total cost price of the whole quantity — not a simple average of the two rates.
Cost of the first lot: 10 kg × ₹38 per kg = ₹380.
Cost of the second lot: 31 kg × ₹46 per kg = ₹1,426.
Total quantity mixed: 10 kg + 31 kg = 41 kg.
Total cost price of the mixture: ₹380 + ₹1,426 = ₹1,806.
Total selling price of the mixture: 41 kg × ₹44 per kg = ₹1,804.
Since the total cost price (₹1,806) is more than the total selling price (₹1,804), the transaction results in a loss of ₹1,806 − ₹1,804 = ₹2.
As an independent check, the mixture's weighted average cost price per kg is (10 × 38 + 31 × 46) ÷ 41 = ₹1,806 ÷ 41 ≈ ₹44.05 per kg, which is about ₹0.05 above the ₹44 per kg selling rate; multiplying this per-kg shortfall by the 41 kg mixture gives the same total loss of ₹2, confirming the result.