**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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hw cn u use 1.4

when profit shud be more than 40%

1+0.4 (profit %) and it is said"atleast 40%" not more than!

At least 40% means that the merchant desires to make a minimum profit of 40%.So ,the profit percentage can either be 40 or more than that.

i didn't under stood why we have used 1.4

40% profit means that 40% more than the cost price which can be divided as 100%+40% .To put them in fractions rather than percentage ,it becomes: 100/100 +40/100=1+0.4=1.4.

For further understanding,go through the concept of multiplying factor.