The number of story books accounts for two-fifths of the total, so the number of story books is 2/5x.

The number of literary books is 20 less than story books, so the number of literary books is (2/5x-20).

The number of science and technology books is three-quarters of that of literature and art books, so the number of science and technology books is [3/4*(2/5x-20)].

Because the total number of books in the corner = story books+literature books+science books.

2/5x+2/5x-20+3/4*(2/5x-20)=x

2/5x+2/5x-20+6/20x-3/4*20=x

Multiply both sides of the equation by 20 and you will get

4 * 2 * x+4 * 2 * x-20 * 20+6 * x-5 * 3 * 20 = 20 * x

8x+8x-400+6x-300=20x

2x=700

x=350

So there are 350 books in the corner.