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. Combining simple ideas from two topics is a very interesting method to create new questio s. This question is from profit and loss combined with the topic progressions.

Question 1: A merchant can buy goods at the rate of Rs. 20 per good. The particular good is part of an overall collection and the value is linked to the number of items that are already on the market. So, the merchant sells the first good for Rs. 2, second one for Rs. 4, third for Rs. 6…and so on. If he wants to make an overall profit of at least 40%, what is the minimum number of goods he should sell?

1. 24
2. 18
3. 27
4. 32

Explanatory Answer

Method of solving this CAT Question from Profit and loss: Sum of n values combined with profit.

Let us assume he buys n goods.
Total CP = 20n
Total SP = 2 + 4 + 6 + 8 ….n terms
Total SP should be at least 40% more than total CP
2 + 4 + 6 + 8 ….n terms ≥ 1.4 * 20 n
2 (1 + 2 + 3 + ….n terms) ≥ 28n
n(n + 1) ≥ 28n
n² + n ≥ 28n
n² - 27n ≥ 0
n ≥ 27

The question is " If he wants to make an overall profit of at least 40%, what is the minimum number of goods he should sell?"
He should sell a minimum of 27 goods.

Hence, the answer is 27.

Choice C is the correct answer.