A shopkeeper bought 20 kg of sugar at ₹45 per kg, 25 kg of sugar at ₹50 per kg…
2022
A shopkeeper bought 20 kg of sugar at ₹45 per kg, 25 kg of sugar at ₹50 per kg and 35 kg of sugar at ₹40 per kg. He spent a sum of ₹450 on transportation and other expenses. He mixed all the three types of sugar and sold all the stock at ₹52.50 per kg. His profit per cent in the entire transaction is
- A.
5%
- B.
4.25%
- C.
6.5%
- D.
7.25%
Show answer & explanation
Correct answer: A
When several batches of the same commodity, bought at different rates, are pooled into one mixed stock and the entire stock is sold at a single uniform price, profit or loss must be worked out on the TOTAL cost versus the TOTAL revenue, not on any one batch's rate. Total Cost Price (CP) = sum of every batch's purchase cost plus any additional expenses (such as transportation); Total Selling Price (SP) = total quantity sold x selling price per unit; Profit % = ((SP - CP) / CP) x 100.
Cost of each batch of sugar: 20 kg x ₹45 = ₹900; 25 kg x ₹50 = ₹1250; 35 kg x ₹40 = ₹1400.
Total cost of the sugar purchased = ₹900 + ₹1250 + ₹1400 = ₹3550.
Add the ₹450 spent on transportation and other expenses: Total Cost Price = ₹3550 + ₹450 = ₹4000.
Total quantity of mixed sugar = 20 + 25 + 35 = 80 kg.
Total Selling Price = 80 kg x ₹52.50 per kg = ₹4200.
Profit = Total SP − Total CP = ₹4200 − ₹4000 = ₹200.
Profit % = (Profit / Total CP) x 100 = (200 / 4000) x 100 = 5%.
Cross-check on a per-kg basis: the weighted-average purchase cost is ₹3550 / 80 kg = ₹44.375 per kg, and the overhead adds ₹450 / 80 kg = ₹5.625 per kg, so the effective cost per kg is ₹44.375 + ₹5.625 = ₹50. Profit per kg = ₹52.50 − ₹50 = ₹2.50, and Profit % = (2.50 / 50) x 100 = 5% — the same result, confirming the answer.