The price of a jewel, passing three hands, rises on the whole by 65%. If the…
2022
The price of a jewel, passing three hands, rises on the whole by 65%. If the first and second sellers earned 20% and 25% profit respectively, find percentage profit earned by the third seller.
Answer: A. 10% — ConceptWhen a price changes through successive transactions, percentage gains are applied multiplicatively to the current price, not added directly to the…
- A.
10%
- B.
15%
- C.
16%
- D.
12%
Show answer & explanation
Correct answer: A
Concept
When a price changes through successive transactions, percentage gains are applied multiplicatively to the current price, not added directly to the original price.
A profit of p% multiplies the current price by (1 + p/100). Therefore, the overall multiplier equals the product of the individual multipliers.
Application
Let the original price be 100 units.
After the first seller earns 20%, the price becomes 100 × 1.20 = 120 units.
After the second seller earns 25%, the price becomes 120 × 1.25 = 150 units.
An overall rise of 65% means the final price is 100 × 1.65 = 165 units.
If the third seller’s profit rate is r%, then 150 × (1 + r/100) = 165. Hence 1 + r/100 = 165/150 = 1.10, so r = 10.
Cross-check
The three multipliers give 1.20 × 1.25 × 1.10 = 1.65, which is exactly a 65% overall rise.
Therefore, the third seller earned a 10% profit.