Question

A library has fiction, non – fiction and reference books. 5/9 of all the books are works of fiction, and 2/15 are works of non – fiction. If there are 7294 reference books, find
the total number of books in the library.

Answer 1

Fiction = 5/9

Non fiction = 2/15

Therefore reference = subtracting sum of fiction and non fiction from total books

Taking common factors of 9 and 15 as 45

Fiction = 25 /45. (Multiplying 5 to both 5 and 9 in 5/9)

Non fiction = 6/45 (Multiplying 3 to both 2 and 15 in 2/15)

Since the books are in fraction

Total books = 1 (whole books of library)

Non reference books = 1 -(25/45+6/45)

= 1-(31/45)=45-31/45= 14/45 (taking denominator 45 as common for subtraction)

Non reference books = 14/45

Number of Non reference books=7294

Therefore 14/45 of x = 7294

x = 7294*45/14 = 23445

Total no of books in library = 23445