Out of total number of students in a college 12% are interested in sports. `3//4` of the total number of students are interested in dancing. 10% of the total number of students are interested in singing and the remaining 15 students are not interested in any of the activities. What is the total number of students in the college?

Options

A. 450
B. 500
C. 600
D. None of these

Answer

To find the total number of students in the college, we can set up the problem using algebra. Let's denote the total number of students as \( x \).

### Step-by-step Solution:

1. **Identify the percentages of students interested in various activities:**
- Students interested in sports: \( 12\% \) of \( x \) = \( 0.12x \)
- Students interested in dancing: \( \frac{3}{4} \) of \( x \) = \( 0.75x \)
- Students interested in singing: \( 10\% \) of \( x \) = \( 0.10x \)

2. **Calculate the total number of students interested in at least one activity:**
- Total students interested in sports, dancing, and singing:
\[ 0.12x + 0.75x + 0.10x = 0.97x \]

3. **Determine the number of students not interested in any activities:**
- According to the problem, there are 15 students who are not interested in any activities. Therefore, the equation becomes:
\[ x - 0.97x = 15 \]

4. **Simplify the equation:**
- This simplifies to:
\[ 0.03x = 15 \]

5. **Solve for \( x \):**
- To find \( x \), divide both sides by \( 0.03 \):
\[ x = \frac{15}{0.03} = 500 \]

6. **Conclusion:**
- The total number of students in the college is \( 500 \).