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A store purchased an article at a wholesale price of $75 and sold it

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A store purchased an article at a wholesale price of $75 and sold it  [#permalink]

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New post Updated on: 12 Aug 2018, 23:54
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e-GMAT Question of the Week #3


A store purchased an article at a wholesale price of $75 and sold it at two successive discounts of 20% and 16.67% respectively, making a profit of 33.3% on the whole price of the article. The store sold another similar article at the same price, making a loss of 33.3% on the whole price. If the second article has a mark-up of 200% over its retail selling price, find by what percentage the mark-up price of 2nd article is more than that of 1st article?

    A. 50
    B. 75
    C. 100
    D. 125
    E. 200


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Originally posted by EgmatQuantExpert on 15 Jun 2018, 05:25.
Last edited by EgmatQuantExpert on 12 Aug 2018, 23:54, edited 3 times in total.
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Re: A store purchased an article at a wholesale price of $75 and sold it  [#permalink]

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New post 15 Jun 2018, 08:02
Long question, long procedure. Took me 5 minutes and I hope my answer is right. I got A as the answer.

(75 *0.8*0.83 (1 + x/100) - 75)/75 = 33.3/100

x = 100.7

Markup is 150 approx.

In the second case, markup is 225.

Thus, 50% increase.

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Re: A store purchased an article at a wholesale price of $75 and sold it  [#permalink]

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New post 15 Jun 2018, 09:03
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EgmatQuantExpert wrote:
e-GMAT Question of the Week #3


A store purchased an article at a wholesale price of $75 and sold it at two successive discounts of 20% and 16.67% respectively, making a profit of 33.3% on the whole price of the article. The store sold another similar article at the same price, making a loss of 33.3% on the whole price. If the second article has a mark-up of 200% over its retail selling price, find by what percentage the mark-up price of 2nd article is more than that of 1st article?

    A. 50
    B. 75
    C. 100
    D. 125
    E. 200



Question could have been written a bit less wordy and clearly..
When you write "another similar article", it is very easy to take the whole price to be same. It could just have been " another article"..
But selling SAME article at SAME price but one making a profit over WHOLE price and other making a loss on WHOLE price means different whole price..
may be you meant retail selling price and not whole price in second case
So let me take it that way...
It's less time consuming if you know..
1) 33.33% is 1/3 and
2) 16.67% is half of above that is 1/6

Successive discounts of 20%(1/5) and 16.67%(1/6) means 4/5 * 5/6 *X=2x/3
33.34 or 1/3 over 75 means 75*4/3=100..
So 2x/3=100...X=150..

Let's work on second..
Same selling price that is 100 gives 33.33% loss means 2y/3 =100..y=150
I suppose the retail selling price is same as whole price here.. so marked price is 200% above 150 and X is also 150..
So it is 200% above X also..

Ans E
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Re: A store purchased an article at a wholesale price of $75 and sold it  [#permalink]

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New post 15 Jun 2018, 09:29
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EgmatQuantExpert wrote:
e-GMAT Question of the Week #3


A store purchased an article at a wholesale price of $75 and sold it at two successive discounts of 20% and 16.67% respectively, making a profit of 33.3% on the whole price of the article. The store sold another similar article at the same price, making a loss of 33.3% on the whole price. If the second article has a mark-up of 200% over its retail selling price, find by what percentage the mark-up price of 2nd article is more than that of 1st article?

    A. 50
    B. 75
    C. 100
    D. 125
    E. 200


Article 1:
Cost (mentioned as wholesale price) = $75
Profit after 2 successive discounts = 33.33% = \(\frac{1}{3}\) of cost.
So, profit = \(\frac{1}{3} * 75\) = $25
So, article 1 was sold at $100.

What was the price quoted (Marked price) for Article 1 before the discounts?
1st discount 20%. So, its price after 1st discount = 80% of Marked price = 4/5 Marked price
2nd discount 16.67% (same as 1/6) of the price after 1st discount.
So, its price after 2nd discount = 1 - \(\frac{1}{6}\) = \(\frac{5}{6}\) of price after 1st discount.
So, final selling price, $100 = \(\frac{4}{5} * \frac{5}{6}\) of Marked price
So, 100 = \(\frac{4}{6}\) of Marked Price
Marked Price of Article 1 = $150. ---- (1)

Article 2: Selling price = $100 (Same as Article 1)
Loss = 33.33% = \(\frac{1}{3}\) of cost.
So, it sold at 1 - \(\frac{1}{3}\) = \(\frac{2}{3}\) of cost = $100.
So, cost of Article 2 = $150

Article 2 had a mark up of 200%.
So, Marked price of Article 2 = 150 + 200% of 150 = $450 --- (2)

Question is how much percentage is (2) more than (1).
$450 is $300 more than $150.
In terms of percentage \(\frac{300}{150}*100\) = 200%

Choice E
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Re: A store purchased an article at a wholesale price of $75 and sold it  [#permalink]

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New post 15 Jun 2018, 23:55
I completely forgot the loss part, the question was so wordy and I was so tired !! Damn it !! ?

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Re: A store purchased an article at a wholesale price of $75 and sold it  [#permalink]

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New post 16 Jun 2018, 11:22
EgmatQuantExpert wrote:

A store purchased an article at a wholesale price of $75 and sold it at two successive discounts of 20% and 16.67% respectively, making a profit of 33.3% on the whole price of the article. The store sold another similar article at the same price, making a loss of 33.3% on the whole price. If the second article has a mark-up of 200% over its retail selling price, find by what percentage the mark-up price of 2nd article is more than that of 1st article?

    A. 50
    B. 75
    C. 100
    D. 125
    E. 200



Concepts regarding Price related Problems:

\(Cost Price < Marked price < Selling Price\)

\(Marked Price = Cost Price + Mark up\)

\(Selling Price = Marked Price - Discounts\)

\(Mark up {%} = {\frac{(Marked Price - Cost Price)}{Cost Price}}*100\)

\(Profit = Selling Price - Cost Price\)

\(Profit {%} = {\frac{Profit}{Cost Price}} * 100\)

\(Profit Margin = {\frac{Profit}{Selling Price}} * 100\)

Now Back to the Question

Given, The Whole sale price of Article 1 = $75

Article 1 is sold at 2 successive discounts as 20% & 16.67%, 20% = 1/5 & 16.67% = 1/6

Let M be the markup on cost price of Article 1,

we have Selling Price of Article 1 as (75 + M)*(1 - 1/5) * (1- 1/6) = (75 + M ) *2/3........(i)

Now Article 1 earned a profit of 33.3% on its whole sale price, hence its Selling price = 75 * (1 + 1/3) = 75 * 4/3 = 100.....(ii)

Equating (i) & (ii), we get (75 + M ) *2/3 = 100

M = 75, hence Marked price of Article 1 = 75 + 75 = 150

Now given that Article 2 is sold at same Selling price, however it earned a loss of 33.3%. Let C be the whole sale price of Article 2, we get

C * (1 - 1/3) = 100

Hence, C = 150

Now also given that the markup on Article 2 is 200%, hence mark up on Article 2 = 150 * 200% = 2 * 150 = 300

Hence Marked price of Article 2 = 150 + 300 = 450

Marked price of Article 2 is more than marked price of article 1 by = 450 - 150 = 300

Hence the difference is in % of marked price of Article 1 = (300/150) * 100 = 200%


Answer E.



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A store purchased an article at a wholesale price of $75 and sold it  [#permalink]

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New post 18 Jun 2018, 06:21
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Solution



Given:
    • A store purchased an article at a wholesale price of $75
    • It sold the article at two successive discounts of 20% and 16.67% respectively
    • In this article, the store made a profit of 33.3% on the whole price
    • The store sold another article at the same of price as the previous one, making a loss of 33.3% on the whole price
    • The second article has a mark-up of 200% over its retail selling price

To find:
    • The percentage by which the mark-up price of the 2nd article is more than that of 1st article

Approach and Working:

Let us consider the case of article 1 first.
    • Wholesale purchase price = $75

As the profit is 33.3% of the wholesale purchase price,
    • Amount of profit = \(33.3% of 75 = 75 * \frac{1}{3} = 25\)
    • Therefore, the selling price = 75 + 25 = 100

Now, this selling price is obtained after two successive discounts of 20% and 16.67%

If we assume the marked price to be x, then we can write
    • \(x * (1 – \frac{20}{100}) * (1 – \frac{16.67}{100}) = 100\)
    Or, \(x * \frac{4}{5} * \frac{5}{6} = 100\)
    Or, \(x * \frac{2}{3} = 100\)
    Or, \(x = 100 * \frac{3}{2} = 150\)

Hence, the mark-up price of the 1st article is $150

Now, let us consider the case of article 2.
    • Selling price of the article = 100

As there is a loss of 33.3% on the whole price, we can write
    • Whole price \(* (1 – \frac{33.3}{100}) = 100\)
    Or, Whole price \(* \frac{2}{3} = 100\)
    Or, Whole price \(= 100 * \frac{3}{2} = 150\)

As there is a mark-up of 200%, we can write
    • The mark-up price = 150 + 200% of 150 = 150 + 300 = 450

Hence, the mark-up price of the 2nd article = $450

    • Therefore, the percentage by which the mark-up price of the 2nd article is more than that of 1st article = \(\frac{450 – 150}{150} * 100 = \frac{300}{150} * 100\) = 200%

Hence, the correct answer is option E.

Answer: E

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Re: A store purchased an article at a wholesale price of $75 and sold it  [#permalink]

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New post 02 Mar 2019, 09:21
EgmatQuantExpert wrote:
e-GMAT Question of the Week #3


A store purchased an article at a wholesale price of $75 and sold it at two successive discounts of 20% and 16.67% respectively, making a profit of 33.3% on the whole price of the article. The store sold another similar article at the same price, making a loss of 33.3% on the whole price. If the second article has a mark-up of 200% over its retail selling price, find by what percentage the mark-up price of 2nd article is more than that of 1st article?

    A. 50
    B. 75
    C. 100
    D. 125
    E. 200



We can let x = the markup price of the 1st article and create the equation (notice that 20% = 1/5, 16.67% = 1/6 and 33.3% = 1/3):

x(1 - 1/5)(1 - 1/6) = 75(1 + 1/3)

x(4/5)(5/6) = 75(4/3)

x(2/3) = 75(4/3)

Multiplying both sides by 3/2, we have:

x = 150

So the markup price of the 1st article is $150. However, its selling price (the price for which it actually sold) is 150(2/3) = $100. Therefore, the 2nd article is also sold for $100. If we let y = the wholesale price of the 2nd article, we have:

100 = y(1 - 1/3)

100 = y(2/3)

150 = y

Now letting z = the markup price of the 2nd article, we have:

z = 150(1 + 2)

z = 150(3)

z = 450

Therefore, the markup price of the 2nd article is $450, which is

(450 - 150)/150 x 100 = 300/150 x 100 = 2 x 100 = 200 percent more than that of the 1st article.

Answer: E
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Re: A store purchased an article at a wholesale price of $75 and sold it   [#permalink] 02 Mar 2019, 09:21
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