A particular library has 75 books

[himu]

A particular library has 75 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month, 65 percent of books that were loaned out are returned and there are 68 books in the special collection at that time, how many books of the special collection were loaned out during that month?

Choices

22
20
16
14
7

[Anurag@Gurome]

A particular library has 75 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month, 65 percent of books that were loaned out are returned and there are 68 books in the special collection at that time, how many books of the special collection were loaned out during that month?

65% of loaned books were returned by the end of the month. Hence, 35% of the loaned books are not in the library by the end of the month.
We know, (75 - 68) = 7 books are not in the library by the end of the month

Hence, 35% of loaned books = 7 books
Hence, number of loaned out books in that month = 7×100/35 = 20

The correct answer is B.

[Ian Stewart]

I like Anurag's solution. Another way is as follows: 65% of the number of loaned books were returned. So 65% of the right answer must be an integer, since you can't return a fraction of a book. So if you multiply the right answer by 65/100 = 13/20, you must get a whole number, and among the answer choices, 20 is the only possibility.