An article is to be sold at a certain price. If it is instead sold at…
2023
An article is to be sold at a certain price. If it is instead sold at two-thirds of that price, there is a loss of 10%.
Find the gain percentage when it is sold at the original price.
Answer: A. 35% — ConceptProfit or loss percentage is measured relative to the cost price (CP). If the selling price (SP) is p% below CP, then SP = (1 - p/100) × CP; if it is…
- A.
35%
- B.
25%
- C.
33%
- D.
30%
Show answer & explanation
Correct answer: A
Concept
Profit or loss percentage is measured relative to the cost price (CP). If the selling price (SP) is p% below CP, then SP = (1 - p/100) × CP; if it is g% above CP, then SP = (1 + g/100) × CP.
Choosing CP = 100 is a valid normalization because all prices scale by the same factor, while the percentages remain unchanged.
Application
Let CP = 100. A loss of 10% means that the reduced selling price is 100 - 10 = 90.
The reduced selling price is two-thirds of the original selling price. Hence (2/3) × original SP = 90.
Original SP = 90 × (3/2) = 135.
Gain = original SP - CP = 135 - 100 = 35.
Gain percentage = (35/100) × 100% = 35%.
Cross-check
Two-thirds of 135 is 90, and 90 is exactly 10% below the cost price 100. Therefore, the gain at the original selling price is 35%.