raju232007 wrote:A merchant sells an item at a 20% discount,but still makes a gross profit of 20% of the cost.What percent of the cost would the gross profit on the item have been if it had been sold without the discount?

A.20%
B.40%
C.50%
D.60%
E.75%

OA is C....Pls explain the logic to solve this problem?

>>you can either solve this using algebraic equations or by taking sample values, I will solve it using the latter
>>lets say 100 is the selling price without any discounts
>>20% discount means 80
>>20% profit means the cost price was 80/1.2 i.e. 200/3
>>Question asks for (gross profit/cost) x 100
>>profit without discount=100-(200/3)
>>we know that the Cost=200/3
>>Answer is 50%

Algebraically,

Let p be price and c be cost.

1. p(0.80) - c = 0.20 c
need profit / c, so (p - c) * 100 /c ?

From 1. p = 1.2*c/0.8 = 12/8 = 3/2c
So p = 3c/2

p - c = 3c/2 - c = 1c/2
So p-c/c = 1/2

50%.