IIT 1998

300 x 5 = 1500 newspapers 1500/60= 25 newspapers. There are 25 newspapers.

Each of the 300 students reads 5 newspapers so the students read $300 \times 5 =1500$ newspapers in all. Since every 60 students read the same newspaper and 1500 newspapers are read in all, there must be $\frac{1500}{60} = \boxed{25}$ different newspapers.

If $300$ students read $5$ newspapers each, then $300 \times 5$ or $1500$ newspapers are read. However, this could mean the same newspaper could be read over and over, so since we know that each newspaper is read by $60$ students, we find that there are $\frac{1500}{60}$ newspapers, or $\boxed{25}$ .