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

What a convoluted question from OG. 'medium difficulty' as per OG but is much more complex.

Kudos for all correct answers

chetan2u

Cost for 65 items= 850/1.5=566
Profit for 65 items = 566*0.5=283
Double Profits=2*283=566
Thus Total cost of classic= total profit of classic =566, Thus total SP for classic= 1132
SP per classic item =850/65*5= 65

Assuming that there is 1 customer of classic and fast fashion, min number of classic pieces per customer =1132/65~17

­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

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

­Hey @saynchalk, 
Since there was a 50% profit markup and SP was $13 so  CP= 13/1.5 is how i got the CP

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.

Posted from my mobile device

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

Vinit800HBS

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

 
­
@Yes2GMAT: 

Simply take the ratio of the 2 equations.

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

\(\frac{1.5 }{ 2 }­ = \frac{65}{ N*5} \)­

\( N = \frac{13 * 2 }{ 1.5} = 17.xx\)­

­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

A clothing retailer used to sell only "fast-fashion" pieces, which were low priced and had a profit markup of 50 percent of the per-item cost (including, for example, the costs of wholesale purchase and marketing). On average, each customer spent $850 annually on around 65 such pieces from the retailer. 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.

The highlighted portion simply means that the company's profit margins are increased exclusively due to a change in markups, and not due to other cost-cutting measures elsewhere (overheads, rent, marketing etc.)

In fast fashion, C was the cost to purchase goods, 850 was the revenue on those goods at 50% markup.
In the classic items, C is still the cost to purchase goods and something greater than 850 will be the revenue on those goods at 100% markup. 

ANSWER 1
This one is straightforward.
Each customer pays $850 per 65 items. Avg: 850/65 = 13.07 = ~13 Remember this. We will need this later....... Statement ( 1 )

ANSWER 2
Let's go step by step. ANSWER 2 asks for a minimum number at which the goal is reached i.e. the profit is doubled.

We are working with Avg here, so we can use a typical customer for all our calculations.

Before we start, let the minimum number be n.

Step 1 - IDENTIFY THE GOAL - The goal here is to double the profit from a customer who was spending $850 per year, who will now spend more money per year.

Step 2 - CALCULATE THE COST AND PROFIT ON 850 AT 50% MARKUP. (Just leave it in fractions for now)

Cost * 1.5 = 850
Cost = 2/3 * 850 .................. Statement ( 2.0 ) 

Profit = 1/3 * 850 .... profit on annual average transations

STEP 3 - CALCULATE THE GOAL 
Goal Profit = 2 * 1/3 * 850 ...... Statement ( 2.1 ) 
Notice that this is equal to the Cost. 

Step 3 - CALCULATE REVENUE TO GENERATE THIS PROFIT BY TWO WAYS - 
Revenue = number of items * cost per item
Revenue = total selling price of all items = cost + markup on cost

The retailer reasons that he can sell more dollars worth of items at a markup double the fast fashion markup.
Fast fashion markup = 50%
Hence, classic piece markup = 100%

From all of this reasoning, we come to understand that the retailer needs to sell goods at a 100% markup such that the cost is same, the price per item is 5 * Avg, the number of items is n and the profits are equal to Goal Profit (statements 1, 2.0 and 2.1)

Piece is all together:

n * 5 * Avg = new revenue per customer

Cost * 2 = Cost + Goal Profit = new revenue per customer (cost + 100% markup on cost = 2 * Cost)

Replace the values from statements 1, 2.0 and 2.1.

n * 5 * 850/65 = 2/3 * 850 * 2
n = 17.33

Rounds off to 17.­

cp: current price
np: new price

nr: new revenue per customer

c: cost


­Customers paid an average of _____13_____ dollars (rounded to the nearest dollar) for each of the retailer's fast-fashion pieces.

cp = \(\frac{850}{65} = 13.07\)


The retailer will need to sell an average minimum of ______17_____ classic pieces per person (rounded to the nearest whole number) to achieve its profit goals for classic pieces.

np = 5 * cp = 5 * 13 = 65

current markup = 50%
=> \(850 = \frac{3}{2} * c\)
=> c = 566.67

new markup = 2 * current markup = 100%
=> nr = 2 * c = 556.67 * 2 = 1133.33

No. of new piece per customer = \(\frac{nr}{np} = \frac{1133.33}{65} = 17.43\)­

some wordings in the passage are quite vague and hard to grasp.
­at first, retailer only sold fast-fashion pieces. Revenue, Cost, and Profits for each item are as follows:

• \(R=\frac{850}{65}\)
• \(C=\frac{850}{65}×\frac{2}{3}\)
• \(P=\frac{850}{65}×\frac{1}{3}\)

now, retailer plans to sell classic pieces. Revenue, Cost, and Profits for each item are as follows:

• \(R'=\frac{850}{65}×5\) (five times what they paid for fast-fashion piece)
• \(C'=\frac{850}{65}×5×\frac{1}{2}\)
• \(P'=\frac{850}{65}×5×\frac{1}{2}\) (double the percentage profit markup per item)

­as we know the company's total costs and the number of customers shall be unchanged, the following must be true:

• \(65×C=850×\frac{2}{3}=n×\frac{850}{65}×5×\frac{1}{2}=n×C'\)

\(n=\frac{13×4}{3}≈17\)
­

Good question

It's about reading comprehension. don't do too much calculation.
price = 850/65 =13.0769
cost = 2/3price = 8.67
markup = 1/3price = 4.3

total cost unchanged which implies that
new cost (per item) * N = 65 pieces * 8.67 (cost per item)


new cost (per item) + new markup = new price (which is 5*$13 as indicated by the question) = $65
new markup = 100% of the new per-item cost (which comes from 'plans to double its percentage profit markup per item')

so new cost = $65/2 = $32.5

thus, $32.5 * N = 65 pieces * 8.67 (cost per item)
N ≈ 17 pieces

Hi,

850/65=13.1 price per product
as 50% markup exists 13.1/1.5=8.7 cost per product 13.1-8.7=4.4 mark-up per product
total profit in 1st case 4.4*65
requested profit for the 2nd case 4.4*65*2
#of products sold*new mark-up per product=4.4*65*2
#of product sold*(13.1*5/2)=4.4*65*2 (new mark-up to be 100% so it is half of the new price)
#of products sold=~17