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

Options

A. at least `30`
B. at most `20`
C. exactly `25`
D. exactly `30`

Answer

To solve the problem, we need to find the number of newspapers given the information about the students and their reading habits.

Let's denote:
- \( N \) as the number of newspapers.
- The total number of students is \( 300 \).
- Each student reads \( 5 \) newspapers.
- Each newspaper is read by \( 60 \) students.

### Step-by-Step Solution:

1. **Calculate the Total Number of Newspaper Readings**:
Each of the \( 300 \) students reads \( 5 \) newspapers. Therefore, the total number of newspaper readings can be calculated as:
\[ \text{Total readings} = \text{Number of students} \times \text{Newspapers read per student} = 300 \times 5 = 1500 \]

2. **Relate Total Readings to Newspapers**:
Each newspaper is read by \( 60 \) students. Therefore, the total number of readings can also be expressed in terms of the number of newspapers \( N \):
\[ \text{Total readings} = \text{Number of newspapers} \times \text{Students reading each newspaper} = N \times 60 \]

3. **Set Up the Equation**:
Since both expressions represent the total number of readings, we can set them equal to each other:
\[ 1500 = N \times 60 \]

4. **Solve for \( N \)**:
To find \( N \), divide both sides of the equation by \( 60 \):
\[ N = \frac{1500}{60} = 25 \]

5. **Conclusion**:
Therefore, the number of newspapers is \( 25 \).

### Final Answer:
The number of newspapers is \( 25 \).