Out of total number of students in a college 12% are interested in sports. `3/4`g 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. Cannot be deterinined

Answer

To solve the problem, we will follow these steps:

### Step 1: Define the total number of students
Let the total number of students in the college be denoted by \( x \).

### Step 2: Calculate the percentage of students interested in each activity
- 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 \( x \) = \( 0.10x \)

### Step 3: Calculate the total percentage of students interested in activities
Now, we will sum up the percentages of students interested in sports, dancing, and singing:
\[ \text{Total percentage} = 12\% + 75\% + 10\% = 97\% \]

### Step 4: Calculate the percentage of students not interested in any activities
The percentage of students not interested in any activities is:
\[ 100\% - 97\% = 3\% \]

### Step 5: Set up the equation for students not interested in any activities
According to the problem, the number of students not interested in any activities is given as 15. Therefore, we can set up the equation:
\[ 3\% \text{ of } x = 15 \]
This can be written mathematically as:
\[ \frac{3}{100} \times x = 15 \]

### Step 6: Solve for \( x \)
To find \( x \), we can rearrange the equation:
\[ x = 15 \times \frac{100}{3} \]
Calculating this gives:
\[ x = 15 \times 33.33 = 500 \]

### Conclusion
Thus, the total number of students in the college is \( \boxed{500} \).

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