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

Question

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

e-GMAT          Question of the Week #3

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SonalSinha803 · Answer

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.

Posted from my mobile device

chetan2u · Answer

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

WizakoBaskar · Answer

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

GyMrAT · Answer

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.

Thanks,
GyM

EgmatQuantExpert · Answer

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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ScottTargetTestPrep · Answer

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

ashikpshetty · Answer

I dont know how everyone here assumed 200% over its retail selling price as 450. Which is wrong, and it should be 300.
And according to this the solution should be 100%.

But now the e-gmat has changed the question, but can someone please verify how everyone assumed the answer correctly.

fireagablast · Answer

This problem is worded increduby confusingly

"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."

So they bought something for $75 (at a wholesale price), then discounted it two more times, and made a profit of 33.33% over the original (pre-wholesale) price? How is that even possible?
75*1/5 = 15 -->75-15=60
60*1/6 = 10 -->60-10 = 50

So they sold it for 50, but somehow made 33.33% profit?

Mansoor50 · Answer

what is "whole price"? is it wholesale?

i really hope gmat does not throw unclear language....wordy i can handle....but wholesale...whole....and a few other phrases that i dont care to remember,,,,,

am moving on the next question!

Balkrishna · Answer

Hi,  ashikpshetty ,  chetan2u   EgmatQuantExpert ,

Yes, I also doubt the official solution.

Regarding 2nd article, the question says that "the second article has a mark-up of 200% over its retail selling price". In the official solution, retail selling price is adopted as 150 whereas retail selling price should be adopted as 100 because 2nd article is sold at 100. I don't know why wholesale price (which is the buying cost of the trader) is considered as the retail price.

I would be grateful if experts make any comment on the above aspect.

Thank you.

Sunil2424 · Answer

Why does the question say markup of 200% over retail selling price specifically. Normally markup is calculated over cost price but this specific wording is causing confusion to me. Since the retail selling price of Article 2 was $100, then the mark up price of article 2 is $300. Then the percentage by which mark up price of Article 2 is more than that of Article 1 is by 100%
Then Ans is C
Request Clarify

rohitagr999 · Answer

This cannot he solved under 2mins.. even with calculator it took me 2mins to solve..

Can we encounter such questions on GMAT? I am having tough time with answering question within 2mins.. my average timing is above 3mins..

Posted from my mobile device

GmatPoint · Answer

The cost price of the article = $75
Let the markup price of the article be MP
Since after giving discounts of 20% and 16.67% on the MP, the store made a profit of 33.3%,
MP* * = $75* 
MP = $150
Selling price of the article = (4/3)*75 = $100

Since for the second article, the SP was the same, and the loss incurred was 33.33%,
The cost price of the second article = $100*(2/3) = $150

If the cost price of the second article is marked up by 200%,
MP = $150*3 = $450.
Thus, the required percentage =  *100 = 200%

Thus, the correct option is E.

RenB · Answer

Hi  ScottTargetTestPrep   Bunuel   chetan2u   KarishmaB ,
Is this question representative of the questions asked in the exam?
GMAT questions are usually clearly worded

KarishmaB · Answer

The question does not make sense to me - not because it is long or convoluted (it is a good idea to solve some convoluted questions to ensure that you understand the concepts really well, even if you would likely not see such questions in the test. Once you ensure that you understand the concepts very well, the test goes very smoothly.) 
The wording is not just ambiguous, but plain wrong in case they mean to say 'retail selling price' is equal to 'wholesale price.' I would never guess that. Also, 'whole' price is not ok. I am guessing that the original poster used some shortcuts here and the actual question is not written like this.

But if you actually try to solve this question (assuming it is written properly), the method will not be that long if you use fraction equivalents.

(1 + \frac{m}{100})(1 - \frac{d}{100}) = (1 + \frac{p}{100} )

(1 + \frac{m}{100}) = \frac{4}{3} * \frac{5}{4} * \frac{6}{5}

(1 + \frac{m}{100}) = 2

So m = 100%

Hence, Marked Price = 2* 75 = 150
Selling price = 75 * (4/3)= 100

For article 2, selling price = 100
Cost price = 100*(3/2) = 150
If we were given that mark up is 200% on cost price of the store, then the marked price = 150*3 = 450

This would give us a 200% increase as the answer.

Purple_Wizard · Answer

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

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

Here the retail selling price is assumed to be the whole price - 150 but technically speaking the RSP should be the price at which it was sold i.e., 100 which would make the mark up price ~300 and hence the answer would be (b) 100%. Most people have made that selection in their response. Such Qs tend to test the language skills rather than the quant skills of the candidates - does GMAC actively address these language concerns?

GangeshChawla · Answer

The retail selling price of the second article is $100 and not $150 (that's the wholesale price; Assuming WSP = Retail Price is wrong obviously). Consequently, if the markup price should be 200% of $100, i.e., $300, the answer should be (300-150)/150*100, which is 100% and not 200%

APram · Answer

Hi,

Can you please clear the doubt that how can the Marked price be considered less than selling price? 
Also in the second part, its saying the article is marked 200% above retail selling price then is it not right to have equation MP2 = 100 + 200% of 100 = 300?

Kinshook · Answer

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?

Article 1: 
Cost price = $75
Sale price = $75(1+33.33%) = $100
Let Mark-up price = x 
x(1-20%)(1-16.67%) = $100
4/5*5/6*x = $100
Mark-up price = x = $150

Article 2: 
Sale price = $100
 Whole price = Retail Selling Price =  $100/(1-33.33%) = $150
Mark-up price = $150 + 200%*$150 = $450

The percentage the mark-up price of 2nd article is more than that of 1st article = (450-150)/150 = 200%

IMO E

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

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