The cost price of an article is 75% of its marked price for sale. How much…
2023
The cost price of an article is 75% of its marked price for sale. How much percent does the tradesman gain after allowing a discount of 15%?
Answer: B. \(13\frac{1}{3}\%\) — ConceptA discount is calculated on the marked price, whereas profit percentage is calculated on the cost price. If the marked price is M and the discount rate…
- A.
20%
- B.
\(13\frac{1}{3}\%\)
- C.
10%
- D.
\(15\frac{2}{3}\%\)
Show answer & explanation
Correct answer: B
Concept
A discount is calculated on the marked price, whereas profit percentage is calculated on the cost price.
If the marked price is M and the discount rate is d%, then selling price = M × (1 − d/100). Gain percentage = ((selling price − cost price) / cost price) × 100.
Application
Let the marked price be 100. The cost price is 75% of 100, so cost price = 75.
After a 15% discount, the selling price is 85% of 100, so selling price = 85.
Profit = selling price − cost price = 85 − 75 = 10.
Gain percentage = (10 / 75) × 100 = \(13\frac{1}{3}\%\).
Cross-check
Increasing the cost price 75 by \(13\frac{1}{3}\%\) adds 10 and gives 85, the same as the discounted selling price.
Therefore, the tradesman gains \(13\frac{1}{3}\%\).