Amit purchased 10 kg of rice at the rate of ₹38 per kg and 31 kg of rice at…
2025
Amit purchased 10 kg of rice at the rate of ₹38 per kg and 31 kg of rice at ₹44 per kg. He sold the whole mixture at the rate of ₹42 per kg. Find his loss (in ₹).
- A.
₹27
- B.
₹30
- C.
₹17
- D.
₹22
Show answer & explanation
Correct answer: D
When lots of goods bought at different rates are mixed and sold together at a single rate, the overall profit or loss is found by comparing the total cost price of the entire mixture with the total selling price of the entire mixture: Loss = Total Cost Price − Total Selling Price (when cost exceeds sale value); Profit = Total Selling Price − Total Cost Price (when sale value exceeds cost).
Cost price of the 10 kg lot = 10 × ₹38 = ₹380.
Cost price of the 31 kg lot = 31 × ₹44 = ₹1,364.
Total cost price of the mixture = ₹380 + ₹1,364 = ₹1,744.
Total quantity of the mixture = 10 kg + 31 kg = 41 kg.
Total selling price of the mixture = 41 kg × ₹42 per kg = ₹1,722.
Since the total cost price (₹1,744) is greater than the total selling price (₹1,722), the transaction results in a loss.
Loss = Total Cost Price − Total Selling Price = ₹1,744 − ₹1,722 = ₹22.
Cross-check: the weighted average cost price per kg of the mixture = ₹1,744 ÷ 41 ≈ ₹42.54 per kg, which is higher than the ₹42 per kg selling price — confirming a loss of about (₹42.54 − ₹42) × 41 kg ≈ ₹22, matching the result above.