Question

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

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
He should sell a minimum of 27 goods.

Answer Choice (C)