72% of the students of a certain class took Biology and 44% took Mathematics. If each student took at least one subject from Biology or Mathematics and 40 took both, then the total number of students in the class is

Options

A. 200
B. 240
C. 250
D. 320

Answer

To solve the problem, we will use the principle of inclusion-exclusion in set theory. Let's denote the total number of students in the class as \( N \).

1. **Identify the percentages and the number of students taking both subjects**:
- Percentage of students taking Biology = 72% of \( N \)
- Percentage of students taking Mathematics = 44% of \( N \)
- Students taking both subjects = 40

2. **Set up the equation using the principle of inclusion-exclusion**:
The formula for the total number of students taking at least one subject is:
\[ \text{Total} = \text{Students taking Biology} + \text{Students taking Mathematics} - \text{Students taking both} \]
Substituting the values we have:
\[ N = 0.72N + 0.44N - 40 \]

3. **Combine like terms**:
\[ N = (0.72 + 0.44)N - 40 \]
\[ N = 1.16N - 40 \]

4. **Rearrange the equation to isolate \( N \)**:
\[ N - 1.16N = -40 \]
\[ -0.16N = -40 \]

5. **Solve for \( N \)**:
\[ N = \frac{-40}{-0.16} \]
\[ N = 250 \]

Thus, the total number of students in the class is **250**.