A grocer bought 32 kg of coffee beans at a price of Rs X per kg. After some…
2025
A grocer bought 32 kg of coffee beans at a price of Rs X per kg. After some time, one-fourth of the stock got spoiled, so he sold the remaining beans at Rs 220 per kg and made a total profit equal to twice the cost price. What is the value of X?
- A.
Rs 60
- B.
Rs 66
- C.
Rs 55
- D.
Rs 50
Attempted by 12 students.
Show answer & explanation
Correct answer: C
Concept: When a profit is described as a multiple of the cost price — here, “twice the cost” — use the identity Profit = Selling Price − Cost Price to write Selling Price = Cost Price + (multiple × Cost Price). Work out the total cost and total selling price for the whole stock, accounting for any spoiled or unsold quantity, then solve the resulting linear equation for the unknown price.
Total stock bought = 32 kg at Rs X per kg, so total cost price, CP = 32X.
Spoiled stock = one-fourth of 32 = 8 kg, so the quantity actually sold = 32 − 8 = 24 kg.
Total selling price of the 24 kg sold at Rs 220 per kg: SP = 24 × 220 = Rs 5280.
The profit is twice the cost price, so Profit = 2 × CP = 2 × 32X = 64X.
Using SP = CP + Profit: 5280 = 32X + 64X = 96X.
Solve for X: X = 5280 ÷ 96 = 55.
Cross-check: With X = 55, CP = 32 × 55 = Rs 1760 and Profit = 2 × 1760 = Rs 3520, so SP should be 1760 + 3520 = Rs 5280 — exactly matching the actual selling price of the 24 kg sold at Rs 220 per kg. So X = Rs 55.
