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 GMATNinjaHighlighted 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)