During a sale, 60% of the goods are sold at a profit of 47%. 40% of the…
2026
During a sale, 60% of the goods are sold at a profit of 47%. 40% of the remaining goods are sold at a profit of 44%, and the rest are sold at a loss of 11%. If all goods have the same cost price, and there is an overall profit of x%, then what is the value of x?
- A.
30.5
- B.
31.5
- C.
32.6
- D.
33.4
Attempted by 20 students.
Show answer & explanation
Correct answer: C
Concept:
When articles that share the same cost price are sold in different quantities at different profit or loss percentages, the overall profit or loss percentage equals the weighted average of the individual percentages, weighted by each segment's fraction of the total quantity (a loss is counted as a negative contribution).
Application:
Assume total goods = 100 units (the cost price per unit is the same throughout, so a base of 100 keeps the arithmetic simple).
First segment: 60% of 100 = 60 units sold at +47% profit.
Remaining goods = 100 − 60 = 40 units. Second segment: 40% of these 40 = 16 units sold at +44% profit.
Third segment: remaining = 40 − 16 = 24 units sold at −11% (a loss).
Profit contribution from each segment: 60 × 47% = 28.2; 16 × 44% = 7.04; 24 × (−11%) = −2.64.
Net profit = 28.2 + 7.04 − 2.64 = 32.6 (on a base of 100), so the overall profit percentage is 32.6%.
Cross-check (fraction/ratio method):
Write each segment as a fraction of the total: 60/100 = 3/5, 16/100 = 4/25, 24/100 = 6/25. Overall percentage = (3/5 × 47) + (4/25 × 44) − (6/25 × 11) = 28.2 + 7.04 − 2.64 = 32.6%, the same result — confirming the answer independently of the assumed base value.
The overall profit is 32.6%, matching the value 32.6 among the given options.