Comprehension:
Read the data given and answer the following questions:
In a class of 60 students:
42 like Mathes,
32 like English,
12 like neither Maths nor English.
How many students like both Maths and English?

Options

A. 28
B. 26
C. 16
D. 12

Answer

To find out how many students like both Maths and English, we can use the principle of inclusion-exclusion.

1. **Identify the total number of students**:
- Total students = 60

2. **Identify the number of students who like Maths**:
- Students who like Maths = 42

3. **Identify the number of students who like English**:
- Students who like English = 32

4. **Identify the number of students who like neither subject**:
- Students who like neither = 12

5. **Calculate the number of students who like at least one subject**:
- Students who like at least one subject = Total students - Students who like neither
- Students who like at least one subject = 60 - 12 = 48

6. **Use the inclusion-exclusion principle**:
- Let \( x \) be the number of students who like both Maths and English.
- According to the principle of inclusion-exclusion:
\[ \text{Students who like at least one subject} = (\text{Students who like Maths}) + (\text{Students who like English}) - (\text{Students who like both}) \]
- Plugging in the values we have:
\[ 48 = 42 + 32 - x \]

7. **Solve for \( x \)**:
- Rearranging the equation gives:
\[ x = 42 + 32 - 48 \]
- Simplifying this:
\[ x = 74 - 48 = 26 \]

8. **Conclusion**:
- Therefore, the number of students who like both Maths and English is **26**.