Doubling the price triples the profit — Aptitude Question
Doubling the price triples the profit: If the selling price is doubled, the profit triples. What is the original… Answer and worked solution on CodeKairo.
- Topic: Profit & Loss
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 105 seconds
Question
If the selling price is doubled, the profit triples. What is the original profit percent?
Options
- 50%
- 66⅔%
- 100%
- 150%
Show the answer and the worked solution
Correct answer: C. 100%
Worked solution
- Let CP = 100 and SP = x. Original profit = x − 100.
- Doubled selling price 2x gives profit 2x − 100.
- Setting 2x − 100 = 3(x − 100) gives 2x − 100 = 3x − 300, so x = 200.
- Profit = 100 on a cost of 100 = 100%.
Answer: 100%.
The idea
Note that doubling the selling price does not double the profit — the cost is unchanged, so the profit more than doubles. Setting CP to 100 keeps the algebra to one line.
Shortcut. Doubling SP adds exactly one SP to the profit, and that addition is 3P − P = 2P. So SP = 2P and CP = SP − P = P: profit equals cost, 100%.
Common trap. 50% — measuring the profit of 100 against the selling price of 200 instead of the cost of 100.