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A bookstore owner bought a shipment of n books at a total cost of E do

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Bunuel
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A bookstore owner bought a shipment of n books at a total cost of E do [#permalink] New post   21 Jan 2021, 00:16
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95% (hard)

Question Stats:

49% (03:07) correct 51% (03:01) wrong based on 83 sessions
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A bookstore owner bought a shipment of n books at a total cost of E dollars, and plans to sell each of the books at the same price and make a 15 percent profit on the entire shipment,. If x of the books were damaged and impossible to sell, how many dollars more than she had originally planned must the owner charge for each of the remaining books in order to make the desired profit on the shipment?

A. \(\frac{1.15E}{n-x}\)

B. \(\frac{1.15Ex}{n(n-x)}\)

C. \(\frac{1.15E}{n(n-x)}\)

D. \(\frac{1.15Ex}{n-x}\)

E. \(\frac{1.15(n-x)}{E}\)
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B
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B
sahilvermani
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Re: A bookstore owner bought a shipment of n books at a total cost of E do [#permalink] New post   21 Jan 2021, 02:08
Selling price of n books 1.15E
Planned SP per book = 1.15E/n

x books were damaged.
New SP per book = 1.15E/(n-x)

So, increment = 1.15E/n - 1.15E/(n-x) = 1.15E [1/n - 1/(n-x)] = 1.15Ex/n(n-x)

So, C.
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stne
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Re: A bookstore owner bought a shipment of n books at a total cost of E do [#permalink] New post   24 Jan 2021, 09:26
sahilvermani wrote:
Selling price of n books 1.15E
Planned SP per book = 1.15E/n

x books were damaged.
New SP per book = 1.15E/(n-x)

So, increment = 1.15E/n - 1.15E/(n-x) = 1.15E [1/n - 1/(n-x)] = 1.15Ex/n(n-x)

So, C.


Hi,sahilvermani,
Good Job, you did everything correct except writing the option. Small typo.
Your answer is B , in error you have written C.
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sahilvermani
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Re: A bookstore owner bought a shipment of n books at a total cost of E do [#permalink] New post   25 Jan 2021, 06:31
stne wrote:
Your answer is B , in error you have written C.

Yep...that's right :blushing:
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Palak74
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Re: A bookstore owner bought a shipment of n books at a total cost of E do [#permalink] New post   24 Mar 2021, 10:19
Total Price that the retailer needs to recover from all N books (including 15% profit) = 1.15E
Price of one book planned =1.15E/n

since X books are damaged

Profit needed remains same but No. of books available to be sold decreases

{1.15E/n + A} (n-x)= 1.15E ------ Main equation to be solved

In the above equation 1.15E/n is the price planned per book
A is the addition needed per book to make up for the loss
n-x is the number of books available to be sold
1.15E is the total amount that is needed.

Solving the equation we get option B

1.15Exn(n−x)1.15Exn(n−x)
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B
salilbagai
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Re: A bookstore owner bought a shipment of n books at a total cost of E do [#permalink] New post   23 Feb 2024, 11:17
sahilvermani wrote:
Selling price of n books 1.15E
Planned SP per book = 1.15E/n

x books were damaged.
New SP per book = 1.15E/(n-x)

So, increment = 1.15E/n - 1.15E/(n-x) = 1.15E [1/n - 1/(n-x)] = 1.15Ex/n(n-x)

So, C.
 

­HI,
A minor mistake in the solution,
So increment = 1.15E/(n-x) - 1.15E/n = 1.15E (1/(n-x) - 1/n) = 1.15E ((n - n +x)/ ((n-x)(n))) = 1.15Ex/(n(n-x))
Ans B
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Re: A bookstore owner bought a shipment of n books at a total cost of E do [#permalink]
23 Feb 2024, 11:17
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