Problem Solving

Hi All,

We're told that a merchant bought an item at a cost of C dollars and marked up its price by 40% - however, the item did not sell and the merchant was forced to discount the price of the item by 20%. We're asked for the percentage profit earned by the merchant by selling the item at the discounted price. Although the prompt does not properly state it, the intent of the question is that the '20% discount' was made to the NEW price (after the 40% mark-up) and not the original price of $C. This question can be approached in a couple of different ways; henilshaht's post shows how easily you can TEST VALUES. You can also approach this Algebraically.

Original Price = $C

The 40% markup would increase the value of C by 40%.... C + (.4)(C) = $1.4(C)

Then the 20% discount on this new price will decrease the value of $1.4(C) by 20%.... $1.4(C) - (.2)($1.4C) = $(1.4)C - $(0.28)C = $1.12C

Since $C increased to $1.12(C), that is a profit of 12%

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

swerve wrote:A merchant bought an item at a cost of c dollars and marked up its price by 40%. However, the item did not sell and the merchant was forced to discount the price of the item by 20%. What was the percentage profit earned by the merchant by selling the item at the discounted price?

A. 8%
B. 12%
C. 20%
D. 28%
E. 32%

The OA is B

Source: e-GMAT

Percent profit is:

Profit/Cost

(R - C)/C

(1.4C*0.8 - C)/C

(1.12C - C)/C = 0.12C/C = 12%

Alternate Solution:

If we let the cost of the item be 100, then the original selling price of the item is 100*1.4 = 140 and the discounted price is 140*0.8 = 112. Since the discounted price yields a profit of 112 - 100 = 12, the profit at the discounted price corresponds to a 12/100 = 12% profit.

Answer: B