Your question seems to be grammatically wrong: have you missed some words? Please check the question again.

From what I understand:
Let the number of books in the shipment be (n)1000 @ $100 each.
Therefore total cost = E = $100,000.

To earn 15 % the books should be sold at $100,000 * 15/100 = $115,000,
Or $115 each book,


Now, say (x)100 books were damaged. So total price to be charged on 900 remaining books to earn 15 % overall profit = $115000/900 = $127.77
Additional price to be charged = $127.77 - $115 = $12.77 each book.(Desired answer)

Now, plug in the values of n, x & E in each equation to get $12.77

In answer B:
1.15Ex/n(n-x) = 1.15 * 100000 * 100/ 1000(1000-100)
= 115000 * 100/ 1000 * 900
= 12.77
Hence, answer is B.

The question is from princeton.
i have copied the question correctly.
OA is B

First, without considering the X damaged books, in order to make 15% profit on all books, the unit selling price of each book should be 1.15E/n. Since X books were damaged, the unit selling price becomes 1.15E/(n-x). So the difference between these two selling prices is the answer:

1.15E/(n-x)-1.15E/n

The answer is 1.15Ex/n(n-x).

Hope my explanation is helpful.