**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?

A. 24

B. 18

C. 27

D. 32

**Correct Answer: (C)**

**
**

**
**
**Explanation:**

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

n^{2}
+ n __>__ 28n

n^{2}
- 27n
__>__ 0

n __>__
27

He should sell a minimum of 27
goods.

**Answer Choice (C)**

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