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

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When sold at a 40% discount, a sweater nets the merchant a 20% profit [#permalink]

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New post 14 Feb 2016, 17:51
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A
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D
E

Difficulty:

  45% (medium)

Question Stats:

64% (01:14) correct 36% (01:40) wrong based on 100 sessions

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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%
[Reveal] Spoiler: OA
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Posts: 5658
Re: When sold at a 40% discount, a sweater nets the merchant a 20% profit [#permalink]

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New post 14 Feb 2016, 18:17
zxcvbnmas wrote:
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%


Hi,
easy Qs.. yes
got to be Careful... YES
we should be careful about what are we measuring % on/what is the base..

let the Marked up price =100..
Selling price= 100-40%of 100=60..
profit= 20%..
therefore the wholesale purchase cost= x.... 1.2x=60
or x=50...
marked price was 100 so 50 over 50...
so answer is 100%..

E
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Re: When sold at a 40% discount, a sweater nets the merchant a 20% profit [#permalink]

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New post 14 Feb 2016, 21:35
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zxcvbnmas wrote:
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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Re: When sold at a 40% discount, a sweater nets the merchant a 20% profit [#permalink]

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New post 14 Feb 2016, 22:07
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%
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Re: When sold at a 40% discount, a sweater nets the merchant a 20% profit [#permalink]

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New post 10 Jan 2018, 18:55
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:
[Reveal] Spoiler:
E


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Re: When sold at a 40% discount, a sweater nets the merchant a 20% profit   [#permalink] 10 Jan 2018, 18:55
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