CAT Quantitative Aptitude Questions | CAT Profit and Loss Questions - Progressions

The question is from CAT Profit and Loss. CAT exam is known to test on basics rather than high funda ideas. CAT also tests multiple ideas in the same question, and 2IIMs CAT question bank provides you with CAT questions that can help you gear for CAT Exam CAT 2023. This question is from profit and loss and discusses about two merchants. If merchant A makes x % profit and merchant B makes y %, then what is the color of the shirt? - that kind of question.

Question 10: Traders A and B buy two goods for Rs. 1000 and Rs. 2000 respectively. Trader A marks his goods up by x%, while trader B marks his goods up by 2x% and offers a discount of x%. If both make the same non-zero profit, find x.

1. 25%
2. 12.5%
3. 37.5%
4. 40%

Video Explanation

Explanatory Answer

Method of solving this CAT Question from Profit and loss: This question is all about forming the right equations.

SP of trader A = 1000 (1 + x).
Profit of trader A = 1000 (1 + x) – 1000.
MP of trader B = 2000 (1 + 2x).
SP of trader B = 2000 (1 + 2x) (1 – x).

Profit of trader B = 2000(1 + 2x) (1 – x) – 2000.
Both make the same profit => 1000(1 + x) – 1000 = 2000(1 + 2x) (1 – x) – 2000
1000x = 2000 – 4000x² + 4000x – 2000x – 2000
4000xx² -1000x = 0
1000x (4x – 1) = 0
=> x = 25%

The question is "If both make the same non-zero profit, find x."

Hence, the answer is 25%.

Choice A is the correct answer.