# 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.
IIM CAT Preparation Tips: Profit and Loss Question

## Aug 24, 2013

### 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.

At 6:03 PM ,  Rajni kant said...

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

At 12:04 AM ,  hemanth said...

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

At 5:54 PM ,  himakrishna chintu said...

i didn't under stood why we have used 1.4