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# A clothing retailer used to sell only "fast-fashion" pieces, which wer

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Re: A clothing retailer used to sell only "fast-fashion" pieces, which wer [#permalink]
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What a convoluted question from OG. 'medium difficulty' as per OG but is much more complex.

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Re: A clothing retailer used to sell only "fast-fashion" pieces, which wer [#permalink]
Sans8, that should be one of the most elegant way to do the question. Kudos for that.
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Re: A clothing retailer used to sell only "fast-fashion" pieces, which wer [#permalink]
Sans8 wrote:
1. Total expenditure per customer = 850$No. of items sold = 65 Amount spent per item = 850$/65 = 13.07$= ~13$

2. Assume,
Total customers = 1(And they're going to remain the same as per question in selling classic pieces)
S.P per item = $13 C.P per item =$13/1.5= $8.67 Profit per item =$4.3
Total profit per customer = Profit per item * Total item sold = $4.3*65 =$281.45
Goal
Total profit = 2*$281.45=$562.9
Profit margin = 100%
S.P for classic Item= 5* S.P of fast fashion = 5*$13 =$65
C.P for classic Item = $65/2=$32.5

Now,
n*(65-32.5)= Total profit for all the items sold of classic
n*32.5 = 562.9
n= 17.32 = ~17

chetan2u Bunuel is there any shorter way to this qstn?­
Question is very dense in order to completely understand what it wants

­Hey I love how much simpler this is than the solution given in the OG. I just wanted to understand how you got the cost price of Classic pieces
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Re: A clothing retailer used to sell only "fast-fashion" pieces, which wer [#permalink]
Statement from the question - Now the retailer wishes to double its total profits by selling only "classic" pieces. It plans to double its percentage profit markup per item and generate more revenue per customer while leaving unchanged the company's total costs. The plan assumes that for each classic piece, on average, customers will pay five times what they paid for each fast-fashion piece, and that the total number of customers for the retailer's clothing products will remain the same.

Double its % profit which means from 50% to 100%, while leaving unchanged the company cost. Which means the earlier cost out of the price of $13 was$8.66. If we Double the profit % we will get the price of the new classic pieces to be ~$16. Then plan assumes that for each classic piece, on average, customers will pay five times what they paid for each fast-fashion piece. In respect to this the customer will now pay 5x13 = 65. Don't you think the language is a bit contradicting in itself, because earlier they said the the cost will remain the same, then said the profit markup will double and then said the customer will pay 5 times the last price. What should be done in questions like these ? Help @martymurphy chetan2u KarishmaB GMATNinja Tutor Joined: 16 Oct 2010 Posts: 14891 Own Kudos [?]: 65406 [5] Given Kudos: 431 Location: Pune, India Re: A clothing retailer used to sell only "fast-fashion" pieces, which wer [#permalink] 5 Kudos Expert Reply Dwadesh72 wrote: Statement from the question - Now the retailer wishes to double its total profits by selling only "classic" pieces. It plans to double its percentage profit markup per item and generate more revenue per customer while leaving unchanged the company's total costs. The plan assumes that for each classic piece, on average, customers will pay five times what they paid for each fast-fashion piece, and that the total number of customers for the retailer's clothing products will remain the same. Double its % profit which means from 50% to 100%, while leaving unchanged the company cost. Which means the earlier cost out of the price of$13 was $8.66. If we Double the profit % we will get the price of the new classic pieces to be ~$16. Then plan assumes that for each classic piece, on average, customers will pay five times what they paid for each fast-fashion piece. In respect to this the customer will now pay 5x13 = 65.

Don't you think the language is a bit contradicting in itself, because earlier they said the the cost will remain the same, then said the profit markup will double and then said the customer will pay 5 times the last price. What should be done in questions like these ?
Help @martymurphy chetan2u KarishmaB GMATNinja

Highlighted is the issue. Cost per piece will not be the same. Overall cost to company will be the same. Cost per piece will be higher but fewer pieces will be bought. After all, we are asked how many classic pieces will each customer buy and that number is far lower than 65.

Here is my evaluation of this tricky question:

On average, each customer spent $850 annually on around 65 such pieces. 50% is profit markup. Selling price per piece = 850/65 =$13 (ANSWER 1)
Revenue (selling price) obtained from each customer = $850 This is CP + 50% of CP =$850
Hence, CP = 566.7 and Profit = $283 per customer. This$283 is what the retailer pockets and wants to double. So he wants a profit of 283*2 = $566 per customer (since he is assuming number of customers stays the same). He will keep a profit percentage markup of 100% on classic pieces so total selling price per customer of classic pieces should be$566*2 = $1133 Selling price per piece for classic items =$13 * 5 = $65 (5 times the selling price of fast fashion) Number of classic peices sold to each customer = 1133/65 = 17 (ANSWER 2)­ Intern Joined: 15 Apr 2021 Posts: 27 Own Kudos [?]: 34 [1] Given Kudos: 496 Re: A clothing retailer used to sell only "fast-fashion" pieces, which wer [#permalink] 1 Kudos saynchalk wrote: Sans8 wrote: 1. Total expenditure per customer = 850$
No. of items sold = 65
Amount spent per item = 850$/65 = 13.07$ = ~13$2. Assume, Total customers = 1(And they're going to remain the same as per question in selling classic pieces) S.P per item =$13
C.P per item = $13/1.5=$8.67
Profit per item = $4.3 Total profit per customer = Profit per item * Total item sold =$4.3*65 = $281.45 Goal Total profit = 2*$281.45= $562.9 Profit margin = 100% S.P for classic Item= 5* S.P of fast fashion = 5*$13 = $65 C.P for classic Item =$65/2=$32.5 Now, n*(65-32.5)= Total profit for all the items sold of classic n*32.5 = 562.9 n= 17.32 = ~17 chetan2u Bunuel is there any shorter way to this qstn?­ Question is very dense in order to completely understand what it wants ­Hey I love how much simpler this is than the solution given in the OG. I just wanted to understand how you got the cost price of Classic pieces ­Hey @saynchalk, Since there was a 50% profit markup and SP was$13 so  CP= 13/1.5 is how i got the CP
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Re: A clothing retailer used to sell only "fast-fashion" pieces, which wer [#permalink]
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Seeing lots of convoluted answers and unnecessary calculations. Here goes a simple approach.

For the first part, it's the total revenue (850) received for 65 fast-piece items. Hence, per item cost to the customer is: 850/65 ~ 13

Now for the second part, let's think some basics first. If the price becomes double, all we have to do is sell only half as many items as before to earn the "same revenue". If the price triples, we have to sell only one-third as many items as before to earn the same revenue.

Now, with that thought in mind, we will also use basic equation for Revenue = Cost + Profit
Currently, we have 50% profit margin.
Hence, Revenue is 1.5CP
Now, we want 100% profit margin.
Hence, Revenue is 2CP

COMBINING THE ABOVE TWO IDEAS,

1.5CP = 65*Price per item
2CP = N * 5*Price per item

Just take the ratio and you will get N ~ 17

Hope that helps.

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Re: A clothing retailer used to sell only "fast-fashion" pieces, which wer [#permalink]
1. 850 / 65 = 13
2. Maintaining the cost while the price is increased 5 fold, so the quantity is = 65/5 = 13
Hold up, he also increase the selling price. initially 1.5*Cost now gone to 2*Cost
Then 13*2/1.5 = 17­
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A clothing retailer used to sell only "fast-fashion" pieces, which wer [#permalink]
Vinit800HBS

How did you solve for N? Isn't there two unknown variables? N and Price for classic ?­
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Re: A clothing retailer used to sell only "fast-fashion" pieces, which wer [#permalink]
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Yes2GMAT wrote:
Vinit800HBS

How did you solve for N? Isn't there two unknown variables? N and Price for classic ?­

­
Quote:
COMBINING THE ABOVE TWO IDEAS,

1.5CP = 65*Price per item
2CP = N * 5*Price per item

Just take the ratio and you will get N ~ 17

@Yes2GMAT:

Simply take the ratio of the 2 equations.

$$\frac{1.5CP }{ 2CP }­ = \frac{65*Price per item }{ N*5*Price per item}$$­

$$\frac{1.5 }{ 2 }­ = \frac{65}{ N*5}$$­

$$N = \frac{13 * 2 }{ 1.5} = 17.xx$$­
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Re: A clothing retailer used to sell only "fast-fashion" pieces, which wer [#permalink]
Sans8 wrote:
1. Total expenditure per customer = 850$No. of items sold = 65 Amount spent per item = 850$/65 = 13.07$= ~13$

2. Assume,
Total customers = 1(And they're going to remain the same as per question in selling classic pieces)
S.P per item = $13 C.P per item =$13/1.5= $8.67 Profit per item =$4.3
Total profit per customer = Profit per item * Total item sold = $4.3*65 =$281.45
Goal
Total profit = 2*$281.45=$562.9
Profit margin = 100%
S.P for classic Item= 5* S.P of fast fashion = 5*$13 =$65
C.P for classic Item = $65/2=$32.5

Now,
n*(65-32.5)= Total profit for all the items sold of classic
n*32.5 = 562.9
n= 17.32 = ~17

chetan2u Bunuel is there any shorter way to this qstn?­
Question is very dense in order to completely understand what it wants

­Thank you for this explanation but can someone explain why S.P for classic Item= 5* S.P of fast fashion? Why are we multiplying with 5?
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Re: A clothing retailer used to sell only "fast-fashion" pieces, which wer [#permalink]
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ridbag wrote:
Sans8 wrote:
1. Total expenditure per customer = 850$No. of items sold = 65 Amount spent per item = 850$/65 = 13.07$= ~13$

2. Assume,
Total customers = 1(And they're going to remain the same as per question in selling classic pieces)
S.P per item = $13 C.P per item =$13/1.5= $8.67 Profit per item =$4.3
Total profit per customer = Profit per item * Total item sold = $4.3*65 =$281.45
Goal
Total profit = 2*$281.45=$562.9
Profit margin = 100%
S.P for classic Item= 5* S.P of fast fashion = 5*$13 =$65
C.P for classic Item = $65/2=$32.5

Now,
n*(65-32.5)= Total profit for all the items sold of classic
n*32.5 = 562.9
n= 17.32 = ~17

chetan2u Bunuel is there any shorter way to this qstn?­
Question is very dense in order to completely understand what it wants

­Thank you for this explanation but can someone explain why S.P for classic Item= 5* S.P of fast fashion? Why are we multiplying with 5?

­Hi ridbag,

It is mentioned in the question: The plan assumes that for each classic piece, on average, customers will pay five times what they paid for each fast-fashion piece
Re: A clothing retailer used to sell only "fast-fashion" pieces, which wer [#permalink]
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