When a producer allows 36% commission on the retail price of his product, he…
2025
When a producer allows 36% commission on the retail price of his product, he earns a profit of 8.8%. What would be his profit if the commission is reduced by 24% ?
- A.
36.6%
- B.
49.6%
- C.
59.6%
- D.
45.6%
Attempted by 16 students.
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Correct answer: B
Solution outline: derive the retail price in terms of cost, then compute the new profit after the reduced commission.
Step 1: Relate retail price and cost.
Let retail price = R and cost = C. After a 36% commission the producer receives 64% of R, so 0.64R = 1.088C. Therefore R = 1.088/0.64 × C = 1.7C.
Step 2: Apply the reduced commission.
A reduction of 24 percentage points turns the commission into 12% of the retail price, so the producer now receives 88% of R (0.88R).
Step 3: Compute the new profit percentage.
New profit = (amount received − cost)/cost = (0.88R − C)/C = 0.88×(R/C) − 1 = 0.88×1.7 − 1 = 1.496 − 1 = 0.496 = 49.6%.
Answer: 49.6%