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?
24
18
27
32

Answer 1

The minimum number of goods he should sell is 27

Solution:

Let "n" be the number of goods he buys

A merchant can buy goods at the rate of Rs. 20 per good

Therefore,

Total cost = 20n

Total Selling Price = 2 + 4 + 6 +  ….n terms

Total SP should be at least 40% more than total CP

$2 + 4 + 6 + 8 . . . n\ terms \geq 1.4 \times 20 n$

$2 (1 + 2 + 3 + ... n\ terms) \geq 28n$

The sum of n terms is $\frac{n(n+1)}{2}$

Therefore,

$2 \times \frac{n(n+1)}{2}\geq 28n\\\\n(n+1)\geq 28n\\\\\n^2 + n\geq 28n\\\\n^2 + n - 28n \geq 0\\\\n^2 -27n\geq 0\\\\n\geq 27$

He should sell a minimum of 27 goods

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