In a college of $300$ students, every student reads $5$ newspapers and every newspaper is read by $60$ students. The number of newspapers is

Each newspaper is read by $60$ students. Then, for $300$ students there would be a need of $\frac{300}{60}=5$.
Now each student is required to read $5$ newspapers.
Hence, total newspapers required in the college will be $5\times 5=25$ newspapers.

$\therefore$ Exactly $25$ newspapers will be required.