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# In a shop, the marked price of an article is worked out in s

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In a shop, the marked price of an article is worked out in s [#permalink]

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31 Oct 2010, 04:30
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65% (01:27) correct 35% (02:30) wrong based on 158 sessions

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In a shop, the marked price of an article is worked out in such a way that it generates a profit of $$33\frac{1}{3}%$$. What should be the discount percent allowed on the marked price during a sale, so that the final profit made is 20%?

A. $$13\frac{1}{3}%$$

B. $$12\frac{1}{2}%$$

C. 10%

D. $$8\frac{1}{2}%$$

E. $$6\frac{2}{3}%$$
[Reveal] Spoiler: OA

Last edited by Bunuel on 24 Apr 2014, 00:58, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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31 Oct 2010, 07:31
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udaymathapati wrote:
Hi, Help me to understand the apprach to this problem..there are no options available

In a shop, mareked price of an article is worked out in such a way that it generates a profit of 33.33%. What should be discount percent allowed on the marked price such that the profit made on the sale of an article is 20%?

Lets say the costr price is x.
Original marked price is (4/3)x for 33.33% profit
New marked price for 20% profit is 1.2x
So the discount = (4/3)x-(1.2)x=(4/3)x-(6/5)x=(2/15)x
Discount as a percentage = $$\frac{2/15 x}{4/3 x} * 100=10%$$
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31 Oct 2010, 18:16
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Let me explain the concept with easier values.
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 5172 times ]

Now, if I go back to your question, let us say the cost price of the item was $100. It was marked up to$133.33 (to generate a profit of 33.33%) but the actual profit received was only 20% i.e. the item was sold at $120. Then, discount % = (133.33 - 120)/133.33 x 100 = 10% Same thing can be done using multipliers (as shrouded1 has done above) When cost price, c, increases by 33.33%, it becomes c + 33.33c/100 = c(1 + 33.33/100) = c4/3. This is the marked price (also called tag price) Profit = 20% so selling price must have been c + 20c/100 = c6/5 Discount = 4c/3 - 6c/5 = 2c/15 Discount is always given on the marked price. Discount % = (2c/15)/(4c/3) x 100 = 10% 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, $$( 1 + \frac{m}{100}) * (1 - \frac{d}{100}) = (1 + \frac{p}{100})$$ If I am to use this formula in your question, $$(1 + \frac{33.33}{100})(1 - \frac{d}{100}) = (1 + \frac{20}{100})$$ $$\frac{4}{3}x (1 - \frac{d}{100}) = \frac{6}{5}$$ d = 10 _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Last edited by VeritasPrepKarishma on 04 Nov 2010, 03:39, edited 1 time in total.
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02 Nov 2010, 03:50
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lets consider the price of an article is : Rs.100... market it for 133.33 so that u get a profit of 13.33 Rs... So now the price of an article is : Rs.133.33
To get profit of 20% of an article ...i.e., 120 is the selling price.. so that you get a profit of 20% on the Rs.100 article...

So you allowed a discount of 133.33 -120.00 = 13.33 on a market price of an article.

for Rs. 133.33 given discount is : 13.33
for 100 what is the discount price???

13.33*100/133.33 = 10%

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03 Nov 2010, 22:19
VeritasPrepKarishma wrote:
Let me explain the concept with easier values.
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

Now, if I go back to your question, let us say the cost price of the item was $100. It was marked up to$133.33 (to generate a profit of 33.33%) but the actual profit received was only 20% i.e. the item was sold at $120. Then, discount % = (133.33 - 120)/133.33 x 100 = 10% Same thing can be done using multipliers (as shrouded1 has done above) When cost price, c, increases by 33.33%, it becomes c + 33.33c/100 = c(1 + 33.33/100) = c4/3. This is the marked price (also called tag price) Profit = 20% so selling price must have been c + 20c/100 = c6/5 Discount = 4c/3 - 6c/5 = 2c/15 Discount is always given on the marked price. Discount % = (2c/15)/(4c/3) x 100 = 10% 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 + m/100) x (1 - d/100) = (1 + p/100) If I am to use this formula in your question, (1 + 33.33/100)(1 - d/100) = (1 + 20/100) 4/3 x (1 - d/100) = 6/5 d = 10 Wow! You explained the concept thoroughly and the way that a newbie can understand it very well. Kudos +1 for such a detailed explanation . Writing the math formulas in a mathematical format will be great for making it visually clear (loved the diagram method). _________________ "I choose to rise after every fall" Target=770 http://challengemba.blogspot.com Kudos?? Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7960 Location: Pune, India Re: Discount Problem [#permalink] ### Show Tags 04 Nov 2010, 03:42 AtifS wrote: Writing the math formulas in a mathematical format will be great for making it visually clear (loved the diagram method). There you go Atif... and yes, I would prefer that one think of the diagram while solving a discount problem rather than the formula. If the concept is clear, no matter how they word the question, it will never be a problem. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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23 Apr 2014, 22:14
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Re: In a shop, the marked price of an article is worked out in s [#permalink]

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26 Apr 2014, 15:33
This one's pretty straightforward.

Let's say the cost is 60 and the original price is 80. Now then we have a projected profit of 33%. If we would like to make only 20% we would have to sell at 72$. Therefore the discount is 8/80=10%. Answer is thus C. Hope its clear Cheers! J Non-Human User Joined: 09 Sep 2013 Posts: 13760 Re: In a shop, the marked price of an article is worked out in s [#permalink] ### Show Tags 14 Jun 2015, 03:09 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Director Joined: 24 Nov 2015 Posts: 584 Location: United States (LA) Re: In a shop, the marked price of an article is worked out in s [#permalink] ### Show Tags 30 Mar 2016, 13:18 lets consider the cost price of an article as$60 (take a number whose 33.33% can be calculated easily)
so marked price = 1.3333*60 = 80
profit to be earned = 20%
final selling price = 1.2*60 = 72
therefore discount to be given = 8/80 = 10%
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In a shop, the marked price of an article is worked out in s [#permalink]

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23 Apr 2017, 05:04
udaymathapati wrote:
In a shop, the marked price of an article is worked out in such a way that it generates a profit of $$33\frac{1}{3}%$$. What should be the discount percent allowed on the marked price during a sale, so that the final profit made is 20%?

A. $$13\frac{1}{3}%$$

B. $$12\frac{1}{2}%$$

C. 10%

D. $$8\frac{1}{2}%$$

E. $$6\frac{2}{3}%$$

Quick way to solve this one..let the price be 1..

$$\frac{4}{3}*x = \frac{6}{5}$$

Solving gives
$$x = 0.9$$

Thus discount = 10%
(C)
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