70% of the cost price of an article is equal to 50% of its selling price. The…
2023
70% of the cost price of an article is equal to 50% of its selling price. The percentage of profit or loss on the cost price is
Answer: C. 40% profit — ConceptProfit or loss is measured relative to cost price (CP), not selling price (SP). If SP > CP, the difference is profit; if SP < CP, it is loss. The rate…
- A.
20% profit
- B.
20% loss
- C.
40% profit
- D.
40% loss
Show answer & explanation
Correct answer: C
Concept
Profit or loss is measured relative to cost price (CP), not selling price (SP).
If SP > CP, the difference is profit; if SP < CP, it is loss. The rate is |SP − CP| / CP × 100%.
Application
Let CP = C and SP = S.
Translate the statement: 70% of C equals 50% of S, so 0.70C = 0.50S.
Divide by 0.50: S = (0.70/0.50)C = 1.40C.
Profit = S − C = 1.40C − C = 0.40C.
Profit percentage = (0.40C/C) × 100% = 40%.
Cross-check
Take C = 100. Then S = 140.
Now 70% of 100 is 70, and 50% of 140 is also 70, so the original relation is satisfied.
Result
The article is sold at a 40% profit.