Today, the mailman sorted 57 letters during his first hour of work, 69 letters during his second hour, 81 letters during his third hour, and 105 letters during his fifth hour. based on the trend, how many letters did the mailman sort during his fourth hour of work?

The answer is 93 

If we sorted out the number of each hours, the sequence will look like this

57 _    69  _  81  _ x  _ 105   

(in which x is the fourth hour of work)

We can see from the sequence that each hours, the mailman add additional 12 letters.
(69 - 57 = 12)
(81 - 69 = 12)   . . . . proof

So, the amount of letters on the fourth hour would be:
81 letters  + 12 letters = 93 Letters

270 books in each shelves