When sold at a 40% discount, a sweater nets the merchant a 20% profit on the wholesale cost at which he initially purchased the item. By what % is the sweater marked up from wholesale at its normal retail price?

A) 20%

B) 40%

C) 50%

D) 80%

E) 100%

Sale Price = Cost + Profit = Marked Price - Discount

Sale Price = Cost * (1 + 20/100) = Marked Price * (1 - 40/100)

Marked Price = 2 * Cost

Marked Price is twice the Cost so this is a 100% mark up.

Answer (E)
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Karishma
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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:

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Rich
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