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

CAT 2021

A
B
C
D
##### 32
Solution

Correct option is

(C)

total CP = 20x

totsl SP = 2+ 4+ 6+ 8 ......x terms

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

2+ 4+ 6+ 8 ....x terms $\geq$ 1.4 * 20x

2(1+2+3+....x terms ) $\geq$ 28x

x(x+1) $\geq$ 28$x$

$x^{2}$ + $x$ $\geq$ 28$x$

$x^{2}$-27$x$ $\geq$ 0

x $\geq$27