When sold at a 40% discount, a sweater nets the merchant a 20% profit

Let C.P. (Cost Price) = c
Let M.P. (Marked Price) = x
=> S.P. (Sale Price) = 0.60x

c + 0.20c = 0.6x
=> c = x/2
=> x = 2c

So, Cost price = c
Marked Price = 2c

Hence, the sweater was marked up 100%

Hi All,

I'm a bit fan of using a combination of TESTing VALUES here (as chetan2u has shown) and that's exactly how I would have solved this problem. It can also be approached with algebra though:

X = wholesale cost of the sweater.

[1 + (N/100)]X = retail price --> N/100 is the percent markup in price

We're told that the sweater is sold at a 40% discount of the retail price, which means that the discount price is 60% of the original retail price. The discounted price of the sweater is:

.6{1 + (N/100)]X

We're told that this price nets the merchant a 20% profit on the wholesale cost, so we have one big equation….

.6[1 + (N/100)]X = 1.2X

Now we can cancel out the Xs:

.6[1 + (N/100)] = 1.2

And do algebra….

[1 + (N/100)] = 2

N/100 = 1

N = 100

Meaning that the original percent markup was 100%

Final Answer:

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

An easy way to solve:

Let wholesale cost price = $x
Assume selling price = $100
Discounted selling price = $60

Profit = (60-x)
It's given that he makes 20% profit on wholesale cost price, which means:

(60-x) / x = 0.20
solving the equation, we get x = wholesale cost price = $50
Since normal retail price is $100, this gives us a markup of 100%.

Answer (E)

chetan2u I understand your explanation up until how to set up the equation for the wholesale cost, if you could explain a little more on how you set that equation up that would be great!

Let’s assume that the wholesale cost of the sweater is $100; thus, the profit on the sale of the sweater is 0.20 x 100 = $20.

If we let x = the original selling price of the sweater, we know that its sale price will be 0.60x, and this sale price will earn for the merchant the original wholesale price of $100 plus the profit of $20. Thus, we have:

0.60x = 120

x = $200

Thus, we see that the original wholesale price was $100, and the original selling price was $200. Therefore, its markup was

(200-100)/100 x 100 = 100%.

Answer: E

# Backsolving
price with 20% profit is 1.2 x Price
40% discount on price is, 0.6 x Price

## Option B, 40%
since, both left side and right side is on an imaginary selling price, we can exclude that from the equation.
1.4 x 0.6 = 1.2
this ain't possible.

## Option D, 80%
1.8 x 0.6 = 1.2
Not this either, but very close though and left side is less than the right side.
Since, lhs < rhs, we need to increase the percentage, and there's only one option with a bigger percentage. That is the answer.

Correct answer is *E*

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