Trader bought bag of kg of basmati rice at Rs.125
A trader bought a bag of 40 kg of basmati rice at Rs.125 per kg and another bag of 60 kg at Rs.150 per kg. He sold the entire stock at a profit of 20%. Find the selling price per kg.
- A.
Rs.152
- B.
Rs.158
- C.
Rs.168
- D.
Rs.172
Attempted by 17 students.
Show answer & explanation
Correct answer: C
Concept: When two lots of the same commodity are bought at different rates, the effective cost price per unit for the mixed stock is the total cost of all the lots divided by their total quantity (a quantity-weighted average, not a plain average of the rates). Applying the profit percentage on this total cost — not on a simple average of the rates — gives the total selling price, which is then divided by the total quantity to get the selling price per unit.
Total cost price of the 40 kg lot = 40 × Rs.125 = Rs.5,000.
Total cost price of the 60 kg lot = 60 × Rs.150 = Rs.9,000.
Combined cost price of the full 100 kg stock = Rs.5,000 + Rs.9,000 = Rs.14,000.
Total selling price at 20% profit = Rs.14,000 × 1.20 = Rs.16,800.
Selling price per kg = Rs.16,800 ÷ 100 kg = Rs.168 per kg.
Cross-check: the overall average cost price per kg is Rs.14,000 ÷ 100 kg = Rs.140 per kg; applying the same 20% margin directly to this average cost gives Rs.140 × 1.20 = Rs.168 per kg — the same result, confirming the answer.