In a college, 40% of the students were allotted group A, 75% of the remaining were given group B and the remaining 12 students were given group C. Then the number of students who applied for the groups is

Options

A. 100
B. 60
C. 80
D. 92

Answer

To solve the problem, let's denote the total number of students who applied for the groups as \( x \).

1. **Calculate the number of students in Group A**:
- According to the problem, 40% of the students were allotted to Group A.
- Therefore, the number of students in Group A is:
\[ \text{Students in Group A} = 0.4x \]

2. **Calculate the remaining students after Group A**:
- The remaining students after allotting Group A can be calculated as:
\[ \text{Remaining students} = x - 0.4x = 0.6x \]

3. **Calculate the number of students in Group B**:
- 75% of the remaining students were allotted to Group B.
- Therefore, the number of students in Group B is:
\[ \text{Students in Group B} = 0.75 \times 0.6x = 0.45x \]

4. **Calculate the remaining students after Groups A and B**:
- The remaining students after allotting Groups A and B can be calculated as:
\[ \text{Remaining students} = 0.6x - 0.45x = 0.15x \]

5. **Set up the equation for Group C**:
- According to the problem, the remaining students who were allotted to Group C are 12.
- Therefore, we can set up the equation:
\[ 0.15x = 12 \]

6. **Solve for \( x \)**:
- To find the total number of students, we can solve the equation:
\[ x = \frac{12}{0.15} = 80 \]

Thus, the total number of students who applied for the groups is **80**.