 # Profit and Loss Question

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

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
n2+ n  > 28n
n2  27n  > 0
n >27
He should sell a minimum of 27 goods.

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1. Rajni kant says:

hw cn u use 1.4
when profit shud be more than 40%

2. hemanth says:

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

1. Gaauri Goel says:

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.

3. himakrishna chintu says:

i didn't under stood why we have used 1.4

4. Gaauri Goel says:

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.