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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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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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Re: Discount Problem [#permalink]

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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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Re: Discount Problem [#permalink]

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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
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
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Last edited by VeritasPrepKarishma on 04 Nov 2010, 03:39, edited 1 time in total.
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Re: Discount Problem [#permalink]

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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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Re: Discount Problem [#permalink]

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New post 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).
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Re: Discount Problem [#permalink]

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New post 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.
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Re: Discount Problem [#permalink]

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New post 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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New post 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

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

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Hello from the GMAT Club BumpBot!

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

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New post 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%
answer - C
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In a shop, the marked price of an article is worked out in s [#permalink]

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New post 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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