What is the total number of students in a college ?
I. 75% of the total number of students are boys.
II. The ratio of number of girls to the number of boys is 1:3.

Options

A. (A). If statement I alone is sufficient but statement II alone is not sufficient.
B. (B). If statement Il alone is sufficient but statement I alone is not sufficient.
C. (C). If each statement alone (either I or II) is sufficient.
D. (D). If statement I and Il together are not sufficient.

Answer

To solve the problem of finding the total number of students in the college, we will analyze the two statements provided and see if they can help us determine the total number of students.

Let’s denote:
- Total number of students = \( x \)
- Number of boys = \( b \)
- Number of girls = \( g \)

### Step 1: Analyze Statement I
Statement I states that 75% of the total number of students are boys.

This can be expressed mathematically as:
\[ b = 0.75x \]
This implies that:
\[ b = \frac{3}{4}x \]

### Step 2: Rearranging Statement I
From the equation \( b = \frac{3}{4}x \), we can express \( x \) in terms of \( b \):
\[ x = \frac{4}{3}b \]

### Step 3: Analyze Statement II
Statement II states that the ratio of the number of girls to the number of boys is 1:3.

This can be expressed as:
\[ \frac{g}{b} = \frac{1}{3} \]
From this, we can derive:
\[ g = \frac{1}{3}b \]

### Step 4: Total Students from Statement II
Now, we can express the total number of students \( x \) in terms of \( b \) and \( g \):
\[ x = b + g \]
Substituting \( g \) from the previous step:
\[ x = b + \frac{1}{3}b = \frac{4}{3}b \]

### Step 5: Combining Both Statements
Both statements lead us to the same equation for \( x \):
\[ x = \frac{4}{3}b \]
However, we do not have a specific value for \( b \) from either statement. Therefore, we cannot determine the exact total number of students \( x \) without knowing the number of boys \( b \).

### Conclusion
Since neither statement alone provides enough information to determine the total number of students, and even when combined, we still lack a specific value for \( b \), we conclude that both statements together are insufficient to answer the question.

Thus, the answer is:
**Both statements together are not sufficient.**