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# A merchant sells an item at a 20% discount, but still makes

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A merchant sells an item at a 20% discount, but still makes [#permalink]

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13 Sep 2007, 23:57
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A merchant sells an item at a 20% 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%
[Reveal] Spoiler: OA

Last edited by Bunuel on 06 Jun 2014, 02:47, edited 1 time in total.
Edited the question and added the OA.
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14 Sep 2007, 00:46
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Cost Price =$y Gross Profits without discount = x-y % of gross profit without discount = (x-y/y)*100 = (x/y -1)*100 With data given we know that: .8x= 1.2y x/y = 3/2=1.5 % of gross profit without discount = (x-y/y)*100 = (x/y -1)*100 = (1.5-1)*100= .5*100=50% Answer C Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 6747 Location: Pune, India Followers: 1874 Kudos [?]: 11527 [2] , given: 219 Re: Merchant Sells Item Discount [#permalink] ### Show Tags 06 Jan 2011, 22:45 2 This post received KUDOS Expert's post 8 This post was BOOKMARKED I have explained the concept below from which we derive the following formula. It makes calculations very simple and you don't need to learn up the formula because it will make sense and stick with you once you go through the explanation: $$( 1 + \frac{m}{100}) * (1 - \frac{d}{100}) = (1 + \frac{p}{100})$$ where m% is mark up %, d% is discount % and p% is profit %. Using the formula to solve your question: If d = 20 and p = 20, $$( 1 + \frac{m}{100}) * (1 - \frac{20}{100}) = (1 + \frac{20}{100})$$ $$( 1 + \frac{m}{100}) * (\frac{4}{5}) = (\frac{6}{5})$$ m = 50 Therefore, the merchant had marked up by 50% which would have been his profit had he not given the discount. Let me explain the concept now. Let us say cost price of an item is$100. I, a merchant, mark it up by 40% and put a tag on it of $140. Now, I have a sale and I offer everything at 10% discount. So something that is marked at$140, will get $14 off and will be sold at$126. The profit I made on the item is $26 (= 126 - 100 (which was my cost price)). This profit is equal to a profit % of 26/100 = 26% (Profit/CP x 100) Note here that my mark up % was 40%, I gave discount of 10% but my profit is only 26%, not 30%. This is because the 40% mark up was on cost price while when I gave discount, I gave 10% on the marked price (which was way more than cost price). The diagram below will make this clearer. Attachment: Ques.jpg [ 13.44 KiB | Viewed 18396 times ] We can make up a quick formula. If m% is the mark up %, d% is the discount % and p% is the profit %, then cost price x ( 1 + m/100) = marked price marked price x (1 - d/100) = selling price which means: cost price x ( 1 + m/100) x (1 - d/100) = selling price We know, cost price x (1 + p/100) = selling price From the 2 equations above, $$( 1 + \frac{m}{100}) * (1 - \frac{d}{100}) = (1 + \frac{p}{100})$$ In other words, when cost price is increased by m% and then decreased by d%, it is equivalent to increasing the cost price by p%. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: Merchant Sells Item Discount [#permalink]

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12 Mar 2011, 08:31
Answer is C.

Lets say

Cost - C
List Price - LP
Selling Price - SP

Profit = SP -C

Profit if sold at 80% of LP = (80LP/100)- C = 20C/100 => 2LP = 3C

Profit if sold at LP = (LP-C/C)*100 = 50%
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Re: Merchant Sells Item Discount [#permalink]

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12 Mar 2011, 09:46
MP = 100

So SP = 80

SP - CP = 0.2CP

So 80 = 1.2CP

So %age = {(100 - 80)/1.2}/80/1.2

= 40/80 = 50%

Answer is C.
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Re: A merchant sells an item at a 20% discount, but still makes [#permalink]

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06 Jun 2014, 02:37
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Re: A merchant sells an item at a 20% discount, but still makes [#permalink]

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06 Jun 2014, 03:15
Let the selling price = 300

Discount = 20% = 60

Received Amount from customer = 240

240 includes 20% profit

Cost price $$= 240 * \frac{120}{100} = 200$$

If no discount given, then shopkeeper would have earned 300 - 200 = 100 on the item costing 200

His "would be" profit percentage $$= \frac{100}{200} * 100 = 50%$$

Answer = C
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Re: A merchant sells an item at a 20% discount, but still makes [#permalink]

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06 Jun 2014, 06:40
Here we can say selling price = s and purchase price or cost is p

it is given in question

.8s = 1.2p

s/p = 1.2/8 = 1.5

say p = 20 , s= 30 we can take any number in this combination.

now 20% discount on 30 i.e. sp is 24 and this is 20% profit on purchase price.

if without discount we sell then 30 is 150 %of 20 so its 50% more then purchase price.

Hope it helps.
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Re: A merchant sells an item at a 20% discount, but still makes [#permalink]

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14 Sep 2015, 13:26
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Re: A merchant sells an item at a 20% discount, but still makes [#permalink]

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04 Nov 2015, 13:19
I did it a bit differently

I first picked a cost = 60

Therefore - GP = 20%cost = 12

Cost + GP = Sale Price = 72

Sale price of 72 represents 80% of Initial cost of the item --> 72/80% = 90

From here i took the 90 as the main Sale price, subtracted cost (60) and got new GP of 30

SP - 90
C - (60)
____
GP - 30

30/60 = 50%
Re: A merchant sells an item at a 20% discount, but still makes   [#permalink] 04 Nov 2015, 13:19
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# A merchant sells an item at a 20% discount, but still makes

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