In a class of 55 students. 40 like Science and 29 like Mathematics. If each student likes at least one subject, answer the following questions.
How many like both Science and Mathematics?

Options

A. 15
B. 14
C. 13
D. 12

Answer

To solve the problem, we need to determine how many students like both Science and Mathematics. We can use the principle of inclusion-exclusion to find the answer.

### Step-by-Step Solution:

1. **Identify the given values:**
- Total number of students (n) = 55
- Number of students who like Science (n(S)) = 40
- Number of students who like Mathematics (n(M)) = 29

2. **Use the formula for the union of two sets:**
The formula for the union of two sets is given by:
\[ n(S \cup M) = n(S) + n(M) - n(S \cap M) \]
where:
- \( n(S \cup M) \) is the number of students who like at least one subject (which is 55 in this case),
- \( n(S) \) is the number of students who like Science,
- \( n(M) \) is the number of students who like Mathematics,
- \( n(S \cap M) \) is the number of students who like both subjects.

3. **Substitute the known values into the formula:**
\[ 55 = 40 + 29 - n(S \cap M) \]

4. **Simplify the equation:**
Combine the numbers on the right side:
\[ 55 = 69 - n(S \cap M) \]

5. **Rearrange to find \( n(S \cap M) \):**
\[ n(S \cap M) = 69 - 55 \]
\[ n(S \cap M) = 14 \]

6. **Conclusion:**
Therefore, the number of students who like both Science and Mathematics is **14**.