Ratio

The Maughan Library recently introduced a collection of books, among which \(30\%\) are Science Fictions, a half are Historical Documents, and the rest are \(60\) Mathematics Literature. Find

1. the ratio of the number of Science Fictions to that of Mathematics Literature in the simplest form,
2. the total number of this collection of books.

A research team borrows some books of Mathematics Literature, and a Science Fiction club borrows some books of Science Fictions from this batch of collection. Assume the number of Historical Documents does not change. The number of Science Fictions and Historical Documents are now in the ratio of $1 : 2\(, while the number of Mathematics Literature and Science Fictions are now in the ratio of $1 : 5\). Find

3. the number of Science Fictions borrowed by the Science Fiction club,
4. the number of Mathematics Literature borrowed by the research team,
5. the new ratio of the number of Science Fictions, Historical Documents and Mathematics Literature.