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A merchant sells an item at a 20 percent discount, but still

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A merchant sells an item at a 20 percent discount, but still [#permalink] New post 28 Jul 2005, 05:04
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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 it had been sold without the discount?

(A) 20 %

(B) 40 %

(C) 50 %

(D) 60 %

(E) 75 %
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 [#permalink] New post 28 Jul 2005, 05:50
let p=price without dicount, c=costs then 0.8p=1,2c and c=0,8p/1,2 which yields 66% for c these are the costs then the gross profit is 34% then the gross profit is 34/66 of the costs or 50%
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 [#permalink] New post 28 Jul 2005, 07:28
Yes it is ~50%.
In cases like this, I suggest to pick the numbers.
Suppose, the price of the item is 100$. After 20% discount it decreases to 80$, and still is the 120% of the cost. if 120% is 80$, than 100% is 66$.
Gross profit per item is 100-66=34.$ The cost is 66$ -> Approx. 50%
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 [#permalink] New post 28 Jul 2005, 08:23
S=sales price
C=cost price

0.8S=1.2C

S=1.5C

s-c=0.5

(s-c)/c *100=50%
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 [#permalink] New post 28 Jul 2005, 08:33
It is exactly 50%

Taking numbers is easy

Should have sold for 100

Sold for 80

20% profit at 80$ for orig cost is 80/1.2 = 200/3

Answer = [100-(200/3)]/200/3=50%
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Re: PS- Costs, Profits and Resale- Tough one. [#permalink] New post 28 Jul 2005, 14:03
mbassmbass04 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 it had been sold without the discount?

(A) 20 %

(B) 40 %

(C) 50 %

(D) 60 %

(E) 75 %



50%
i pick numbers cost 1OO
Hence the sell price given he made a gross profit of 20 percent of the cost.
is 120
Those 12O is a 20% discount
so 120 IS 80/1OO of X
hence without discount the price is 150
GROSS PROFIT IS 5O (150- 100)
COST 1OO
50/1OO= 50 %
:wink:
Re: PS- Costs, Profits and Resale- Tough one.   [#permalink] 28 Jul 2005, 14:03
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A merchant sells an item at a 20 percent discount, but still

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