Solution: Assuming that the original library has X science and technology books, then the original story book is 3x/2. Set up a new science and technology book ***y, and then buy a new story book y- 100.

According to the arrangement in the morning, the book ratio of science and technology books to story books is 10:9. )

(x+y):(3x/2)= 10:9。 After sorting: 9(x+y)- 10(3x/2)=0.

Put them into the library according to the newly bought story books in the afternoon. The ratio of these science and technology books to story books is 5:6. )

(x+y):(3x/2+y- 100)=5:6。 After finishing, it is: 6(x+y)-5(3x/2+y- 100)=0.

Make the above two equations into equations and then solve the equations.

The equation 1 is simplified to -2x+3y=0.

The simplified equation is-1.5x+y=-500.

Multiply equation 2 by 3 and subtract 1 to get x=600.

Take it into the equation 1 and you get y=400.

Then find 3x/2=900.

There are 600 science and technology books and 900 story books in the library.