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

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Joined: 08 Jun 2005
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A merchant sells an item at a 20% discount, but still makes  [#permalink]

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Updated on: 06 Jun 2014, 02:47
22
00:00

Difficulty:

55% (hard)

Question Stats:

69% (02:08) correct 31% (02:20) wrong based on 475 sessions

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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%

Originally posted by KillerSquirrel on 13 Sep 2007, 23:57.
Last edited by Bunuel on 06 Jun 2014, 02:47, edited 1 time in total.
Edited the question and added the OA.
Veritas Prep GMAT Instructor
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Location: Pune, India
Re: Merchant Sells Item Discount  [#permalink]

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06 Jan 2011, 22:45
6
11
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 100840 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%.
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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 Director Joined: 01 Feb 2011 Posts: 668 Re: Merchant Sells Item Discount [#permalink] ### Show Tags 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% Retired Moderator Joined: 16 Nov 2010 Posts: 1436 Location: United States (IN) Concentration: Strategy, Technology Re: Merchant Sells Item Discount [#permalink] ### Show Tags 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. _________________ Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant) GMAT Club Premium Membership - big benefits and savings SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1829 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) Re: A merchant sells an item at a 20% discount, but still makes [#permalink] ### Show Tags 06 Jun 2014, 03:15 2 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 _________________ Kindly press "+1 Kudos" to appreciate Manager Joined: 10 Mar 2014 Posts: 199 Re: A merchant sells an item at a 20% discount, but still makes [#permalink] ### Show Tags 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. Manager Joined: 23 Sep 2015 Posts: 85 Concentration: General Management, Finance GMAT 1: 680 Q46 V38 GMAT 2: 690 Q47 V38 GPA: 3.5 Re: A merchant sells an item at a 20% discount, but still makes [#permalink] ### Show Tags 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% Intern Joined: 28 Feb 2017 Posts: 4 Re: A merchant sells an item at a 20% discount, but still makes [#permalink] ### Show Tags 29 Jan 2018, 08:14 Honestly its very easy question provided you pick the right numbers Lets assume the SP is 120. So offering a 20% discount, the merchant sells at 96 and on this he make a 20% profit. So his cost is 80. Now of if he sells without the discount then the profit on cost would be 120-80/80 = 50%.. Should be able to do it under 1 min though EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 12687 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: A merchant sells an item at a 20% discount, but still makes [#permalink] ### Show Tags 28 Feb 2018, 22:18 Hi All, This question is perfect for TESTing VALUES, but you have to be very careful about how you do the math. Let's break this into pieces... A merchant sells an item at a discount and makes a gross profit of 20% on the cost. Let's TEST VALUES: Cost =$100
Discount Price = $120 Here we have a 20% profit on the cost... Regular Price =$X

Now, let's factor in the fact that the sale price was a 20% discount...

$120 = X - (.2)(X)$120 = .8X
$1200 = 8X$150 = X

So, the regular price was $150. We're asked what the profit would have been WITHOUT the discount: Cost:$100
Regular Price = $150 Profit = (150 - 100)/100 = 50/100 = 50% Final Answer: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: A merchant sells an item at a 20% discount, but still makes  [#permalink]

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19 Jun 2018, 12:59
1
KillerSquirrel wrote:
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%

I am going to tell you an amazing way to do this in matter of 10 seconds. Please have patience with me and see below. Once you grab the concept profit loss and mixtures questions will become your strongest points.

120/100 = 80/100 * x

if you do basic calculations X is 3/2
This means 50% increase. This is the answer

how I did it? See when we say he gave a discount of 20% , it is upon some value be it 100 or 50 or 25 or 78 or 10000 --- > so 20% discount means he sold at 80% of the value? got it? see how.

100-20 / 100 = 0.8,
50-10/50 = 0.8

take any value the ratio will be 8/10
now we can see he clearly made a loss but must have done something that resulted in 20% overall profit. Right? That something is x in the equation.

so that X is your answer when he doesn't give the discount.

In short, no need to take values as left hand common part will be cancelled with right side of equation.

Good Luck
Re: A merchant sells an item at a 20% discount, but still makes &nbs [#permalink] 19 Jun 2018, 12:59
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