A Grocer bought 24 kg coffee beans at price X per kg. After a while one third…
2024
A Grocer bought 24 kg coffee beans at price X per kg. After a while one third of stock got spoiled so he sold the rest for Rs. 200 per kg and made a total profit of twice the cost. What must be the price of X?
- A.
Rs. 33 + (1/3)
- B.
Rs. 66 + (2/3)
- C.
Rs. 44 + (4/9)
- D.
Rs. 50 + (1/3)
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Correct answer: C
Key idea: the revenue from the unsold (non-spoiled) stock equals three times the total cost because the profit is twice the cost.
Total quantity purchased = 24 kg. One third is spoiled, so remaining quantity = 24 × (2/3) = 16 kg.
Selling price for remaining stock = 200 per kg, so total revenue = 16 × 200 = 3200.
Let cost price per kg be X. Total cost = 24 × X. Profit is twice the cost, so profit = 2 × total cost and revenue = total cost + profit = 3 × total cost.
Set up the equation: 3200 = 3 × (24X) = 72X. Solve: X = 3200/72 = 400/9 = 44 + 4/9.
Answer: Rs. 44 + 4/9 per kg.