In a class of 60 students, 30 students like Mathematics, 25 like Science and 15 like both. Then, the number of students who like either Mathematics or Science is

Options

A. 30
B. 40
C. 45
D. 50

Answer

To solve the problem, we need to find the number of students who like either Mathematics or Science in a class of 60 students, where:

- Number of students who like Mathematics (M) = 30
- Number of students who like Science (S) = 25
- Number of students who like both subjects (M ∩ S) = 15

We can use the principle of inclusion-exclusion to find the total number of students who like either Mathematics or Science (M ∪ S).

### Step-by-step Solution:

1. **Identify the given values**:
- Let \( M \) = Number of students who like Mathematics = 30
- Let \( S \) = Number of students who like Science = 25
- Let \( M \cap S \) = Number of students who like both Mathematics and Science = 15

2. **Use the formula for the union of two sets**:
The formula for the number of elements in the union of two sets is:
\[ M \cup S = M + S - M \cap S \]

3. **Substitute the values into the formula**:
\[ M \cup S = 30 + 25 - 15 \]

4. **Calculate the result**:
\[ M \cup S = 55 - 15 = 40 \]

5. **Conclusion**:
The number of students who like either Mathematics or Science is 40.

### Final Answer:
The number of students who like either Mathematics or Science is **40**.

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