In a colleage of 300 students, every student reads 6 newspaper and every newspaper is read by 72 students. The no. 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 in a college where every student reads 6 newspapers and each newspaper is read by 72 students.

Let's break down the solution step by step:

### Step 1: Understand the given information
- Total number of students (S) = 300
- Each student reads (N) = 6 newspapers
- Each newspaper is read by (R) = 72 students

### Step 2: Calculate the total number of newspaper readings
The total number of readings can be calculated by multiplying the total number of students by the number of newspapers each student reads:
\[ \text{Total readings} = S \times N = 300 \times 6 = 1800 \]

### Step 3: Set up the equation for the number of newspapers
Let the number of newspapers be \( x \). Since each newspaper is read by 72 students, the total number of readings can also be expressed as:
\[ \text{Total readings} = x \times R = x \times 72 \]

### Step 4: Equate the two expressions for total readings
Now we can set the two expressions for total readings equal to each other:
\[ 300 \times 6 = x \times 72 \]

### Step 5: Solve for \( x \)
Substituting the values we calculated:
\[ 1800 = x \times 72 \]
To find \( x \), divide both sides by 72:
\[ x = \frac{1800}{72} \]

### Step 6: Calculate \( x \)
Now perform the division:
\[ x = 25 \]

### Conclusion
The number of newspapers is \( x = 25 \).