First, it is divided into two steps. Step one, I haven't bought a science book yet. Let the number of literary books be x, then the number of scientific books is 4X/5.

You can get X+4X/5=5400 and X=3000, that is, 3000 literature books and 2400 science books.

The second is to buy another science and technology book, and the science and technology book bought in sets is Y.

Available (2400+Y)/3000=9/ 10, and Y=300, that is, the library bought 300 science and technology books.