In a sale, all goods have the same cost price per unit. Of these goods, 45%…
2026
In a sale, all goods have the same cost price per unit. Of these goods, 45% are sold at a profit of 32%. Of the remaining goods, 20% are sold at a profit of 46%, and the rest are sold at a loss of 24%. If the overall profit is x%, find x.
Answer: D. 8.9 — ConceptWhen equal-cost units are sold at different profit or loss rates, the overall percentage is the weighted average of their signed rates. Use one common…
- A.
14.5
- B.
15
- C.
7
- D.
8.9
Attempted by 17 students.
Show answer & explanation
Correct answer: D
Concept
When equal-cost units are sold at different profit or loss rates, the overall percentage is the weighted average of their signed rates.
Use one common cost base, multiply each group's share by its signed percentage, and add the contributions.
Application
Take the total cost price of 100 equal-cost units as 100.
The first 45 units contribute a profit of 45 × 32/100 = 14.40.
After 45 units, 55 units remain. Twenty percent of 55 is 11, so these 11 units contribute a profit of 11 × 46/100 = 5.06.
The final 55 − 11 = 44 units are sold at a loss and contribute −(44 × 24/100) = −10.56.
Net profit = 14.40 + 5.06 − 10.56 = 8.90 on a cost base of 100.
Cross-check
The three selling amounts are 59.40, 16.06, and 33.44. Their sum is 108.90, which is 8.90 more than the cost base of 100.
Result
Therefore, x = 8.9.