A retailer marks all his goods at 50% above the cost price and, thinking that…
2022
A retailer marks all his goods at 50% above the cost price and, thinking that he will still make 25% profit, offers a discount of 25% on the marked price. What is the actual profit he earns on his sales?
Answer: C. 12.50% — ConceptSuccessive percentage changes act on different bases, so their rates cannot be added or subtracted directly. If cost price is CP, marked price is CP ×…
- A.
95%
- B.
12%
- C.
12.50%
- D.
15%
Show answer & explanation
Correct answer: C
Concept
Successive percentage changes act on different bases, so their rates cannot be added or subtracted directly.
If cost price is CP, marked price is CP × (1 + markup rate), and selling price is marked price × (1 − discount rate). Profit percent is (SP − CP) / CP × 100.
Application
Let the cost price be 100. A 50% markup gives a marked price of 100 × 1.50 = 150.
A 25% discount on 150 is 150 × 0.25 = 37.50, so the selling price is 150 − 37.50 = 112.50.
Profit is 112.50 − 100 = 12.50. Therefore, profit percent is 12.50 / 100 × 100 = 12.50%.
Cross-check
Combine the multipliers: SP / CP = 1.50 × 0.75 = 1.125.
Therefore SP is 112.5% of CP, so the remaining 12.5% is profit.
The actual profit is 12.50%.