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A merchant sells an item at a 20% discount, but still makes a gross pr
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Updated on: 20 Feb 2019, 04:15
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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% Project PS Butler : Question #33 Subscribe to get Daily Email  Click Here  Subscribe via RSS  RSS
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Originally posted by KillerSquirrel on 13 Sep 2007, 23:57.
Last edited by Bunuel on 20 Feb 2019, 04:15, edited 3 times in total.
Renamed the topic and edited the question.




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Re: A merchant sells an item at a 20% discount, but still makes a gross pr
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06 Jan 2011, 22:45
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 145066 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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Re: A merchant sells an item at a 20% discount, but still makes a gross pr
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14 Sep 2007, 00:46
regular price = $100
discounted price = $100  20% = $80
c + .2c = 1.2c = 80
c = 66.6
if sold at regular price, profit is 10066.66 = 33.33
33.33/66.66 = 50% (C)




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Re: A merchant sells an item at a 20% discount, but still makes a gross pr
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14 Sep 2007, 09:18
Let the Market Price of the product is MP.
Let the Original Cost Price of the product is CP.
Selling Price (Discounted Price) = 100%of MP  20%MP
= 80% of MP.  (1)
Profit made by selling at discounted price = 20% of CP  (2)
Apply the formula:
Profit = Selling Price  Original Cost Price
=> 20% of CP = 80% of MP  100% CP
=> MP = 120CP/80 = 3/2 (CP)
Now if Product is sold without any discount, then,
Profit = Selling Price (without discount)  Original Cost Price
= Market Price  Original Cost Price
= MP  CP
= 3/2 CP  CP
= 1/2 CP
= 50% of CP
Thus, Answer should be C.
Nice question.
 Brajesh



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Re: A merchant sells an item at a 20% discount, but still makes a gross pr
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14 Sep 2007, 09:29
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%
C
assume its 100 before discount.
so it was sold at 80 .
still gross profit of 20 means . original cost was 80 *( 100/120) = 200/3
if no discount it would have been sold at 100
so profit [100 200/3] / [200/3 ] * 100 = 50%



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Re: A merchant sells an item at a 20% discount, but still makes a gross pr
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14 Sep 2007, 14:13
Killersquirrel
What is the answer to this question
I have spent over 30 mins and still no where
Cost = 100
selling price 80
Based on the profit should be negative
If he is still making 20 % profit
if SP < Cost then it can never be a profit?
am I missing something her?



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Re: A merchant sells an item at a 20% discount, but still makes a gross pr
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14 Sep 2007, 14:34
the OA is (C)
The "trick" is to find the original cost > C
80Cost = Profit
P/C = 20/100
(80C)/C = 20/100
80C = 1/5*C
80 = 1/5*C+C
80 = 6/5*C
400 = 6*C
C = ~67
hence > 10067=33 > 33/67 = ~50



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Re: A merchant sells an item at a 20% discount, but still makes a gross pr
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14 Sep 2007, 15:03
S: selling price
C: cost
0.8S  C = 0.2C > 0.8 S = 1.2 C > S = 1.5 C
S  C = 1.5 C  C = 0.5 C
ANS: C [50%]



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Re: A merchant sells an item at a 20% discount, but still makes a gross pr
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05 Jan 2011, 06:48
Ans: C
Suppose the cost price as 100.
The managed to sold it with 20% profit. Thus, he sold it for 120.
And 120 was the discounted rate of 20%. 120 is 80% of 150.
So, the marked price was 150, selling at which would incur a good profit of 50%.



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Re: A merchant sells an item at a 20% discount, but still makes a gross pr
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05 Jan 2011, 12:43
Let the selling price without discount = $x
Cost Price =$y
Gross Profits without discount = xy
% of gross profit without discount = (xy/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 = (xy/y)*100 = (x/y 1)*100 = (1.51)*100= .5*100=50%
Answer C



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Re: A merchant sells an item at a 20% discount, but still makes a gross pr
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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 = (LPC/C)*100 = 50%



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Re: A merchant sells an item at a 20% discount, but still makes a gross pr
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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 a gross pr
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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 a gross pr
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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 a gross pr
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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%



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Re: A merchant sells an item at a 20% discount, but still makes a gross pr
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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 12080/80 = 50%.. Should be able to do it under 1 min though



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Re: A merchant sells an item at a 20% discount, but still makes a gross pr
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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
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Re: A merchant sells an item at a 20% discount, but still makes a gross pr
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19 Jun 2018, 12:59
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. 10020 / 100 = 0.8, 5010/50 = 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



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Re: A merchant sells an item at a 20% discount, but still makes a gross pr
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09 Feb 2019, 07:59
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%
These types do take a toil of me So Profit was 20% will mean that IF the initial cost was $100, profit will make the selling cost to $120 Now this $120 was 20 % discounted value of some value that value = 150 *20/100 = 30 150100 =50 % C
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Re: A merchant sells an item at a 20% discount, but still makes a gross pr
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09 Feb 2019, 19:56
Go the opposite way if your percentage skills are strong. Let the original price be 100$. The end profit made by merchant is 20%. That means it was sold for 120$. Now this amount is the discounted amount (by 20%). That means it was marked up by 25% (Concept: if A is less than B by 20%, then B is greater than A by 25%). Therefore, 25% of 120$ is 30$. The amount on which the discount was provided= 120 + 30 = 150$ (which is 50% increase in the cost price) Answer is C.




Re: A merchant sells an item at a 20% discount, but still makes a gross pr
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