Because this topic has two different individuals, it is most appropriate to take the same book as "1" last time. Then the book 1 * * * is "2" units.

So before b publishes the book:

B Books with1÷ (1-1/4) =1÷ 3/4 = 4/3 units.

A has 2-4/3=6/3-4/3=2/3 units of books.

So before A gives B a book:

A book with 2/3 ÷ (1-1/5) = 2/3 ÷ 4/5 = 2/3× 5/4 = 5/6 units.

So B has 2-5/6=7/6 units of books.

So:

The book ratio of A and B is 5/6: 7/6 =5:7.