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

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

n² + n  > 28n

n² -  27n  > 0

n > 27

He should sell a minimum of 27 goods.

Answer Choice (C)

CAT - Profit and Loss Simple Question

Question

Traders A and B buy two goods for Rs. 1000 and Rs. 2000 respectively. Trader A marks his goods up by x%, while trader B marks his goods up by 2x% and offers a discount of x%. If both make the same profit, find x

A.      25%

B.      12.5%

C.      37.5%

D.      40%

Answer Choice: (A)

Explanatory Answer:

SP of trader A = 1000 (1 + x)

Profit of trader A = 1000 (1 + x) - 1000

MP of trader B = 2000 (1 + 2x)

SP of trader B = 2000 (1 + 2x) (1 - x)

Profit of trader B = 2000(1 + 2x) (1 - x)- 2000

Both make the same profit => 1000(1 + x) – 1000 = 2000(1 + 2x) (1 - x)- 2000

1000x = 2000 – 4000x² + 4000x – 2000x - 2000

4000x² -1000x = 0

1000x (4x - 1) = 0

ð  x = 25%

Answer Choice (A)