What is the actual profit when the profit on the selling price is 25%?
2020
What is the actual profit when the profit on the selling price is 25%?
- A.
33.33%
- B.
30.33%
- C.
25%
- D.
20%
Attempted by 2 students.
Show answer & explanation
Correct answer: A
Concept
Profit percentage is conventionally measured on the COST price (CP) — that is the "actual" profit. When a problem instead states profit as a percentage of the SELLING price (SP), the base is different, so the two percentages are NOT the same. To convert, set up SP = CP + Profit and re-express the profit against CP.
Application
Let SP = 100 (a convenient base).
Profit on SP = 25%, so Profit = 25% of 100 = 25.
Since SP = CP + Profit, CP = 100 − 25 = 75.
Actual profit % (on CP) = Profit / CP × 100 = 25 / 75 × 100 = 100/3 = 33.33% (a recurring decimal, i.e. 33⅓%).
Cross-check
Reverse it: a 33⅓% (33.33%) profit on CP = 75 gives Profit = 75 × 1/3 = 25 and SP = 75 + 25 = 100; then profit as a fraction of SP = 25/100 = 25%, matching the given data. So the actual profit is 33⅓% (33.33%).