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

a)20%
b)40%
c)50%
d)60%
e)75%

Let the cost = $100.
We can PLUG IN THE ANSWERS, which represent the profit without the discount.
When the correct answer choice is plugged in, the discounted selling price will yield a 20% profit, implying a discounted selling price of $120.

Answer choice D: 60% profit without the discount
60% of 100 = $60, implying a regular selling price of $160.
Selling price with a 20% discount = 160 - 20% of 160 = 160-32 = 128.
The discounted price is too great.
Eliminate D.

Answer choice B: 40% profit without the discount
40% of 100 = $40, implying a regular selling price of $140.
Selling price with a 20% discount = 140 - 20% of 140 = 140-28 = 112.
The discounted price is too small.
Eliminate B.

Since D yields a discounted price that is too great, while B yields a discounted price that is too small, the correct answer choice must be between D and B.

The correct answer is C.

Answer choice C: 50% profit without the discount
50% of 100 = $50, implying a regular selling price of $150.
Selling price with a 20% discount = 150 - 20% of 150 = 150-30 = 120.
Success!

Very Simple...........
Let after discount Profit+Cost = 120
So the mark price will be
120/80 * 100 =150
It means 50% profit will be if there is no discount

Wouldn't hurt to learn the algebra here either, so let's add that approach.

There are three prices to consider: the full price, the discounted price, and the merchant's cost.

Let's say the cost is x.

We know the discounted price is 20% GREATER than the cost, so that's x + (20% of x), or 1.2x.

We know the discounted price is 20% LESS than the full price. That means 1.2x = (80% of full price), or 1.2x = .8f, or 12x = 8f, or f = 1.5x. So the full price is 1.5x.

Since the cost is x, and the full price is 1.5x, the profit would be .5x, or 50% of x.