In a school 80 students like chocolate, 40 like coffee if the number of students doesn't like any of them is equal to the number of students who like both of them then what is the total number of students in the school?

Options

A. 115
B. 90
C. 120
D. None of these

Answer

To solve the problem step by step, we will denote:

- Let \( A \) be the set of students who like chocolate.
- Let \( B \) be the set of students who like coffee.
- Let \( n(A) \) be the number of students who like chocolate = 80.
- Let \( n(B) \) be the number of students who like coffee = 40.
- Let \( n(A \cap B) \) be the number of students who like both chocolate and coffee.
- Let \( n(A \cup B) \) be the number of students who like either chocolate or coffee (or both).
- Let \( x \) be the number of students who like both chocolate and coffee.

According to the problem, the number of students who do not like either chocolate or coffee is equal to the number of students who like both. Therefore, we have:

1. **Step 1: Set up the equation for total students.**
The total number of students in the school can be expressed as:
\[ n = n(A \cup B) + \text{students who do not like either} \]
Since the students who do not like either is equal to \( x \) (the number of students who like both), we can rewrite this as:
\[ n = n(A \cup B) + x \]

2. **Step 2: Use the formula for the union of two sets.**
The formula for the union of two sets is given by:
\[ n(A \cup B) = n(A) + n(B) - n(A \cap B) \]
Substituting the known values:
\[ n(A \cup B) = 80 + 40 - x = 120 - x \]

3. **Step 3: Substitute into the total students equation.**
Now substituting \( n(A \cup B) \) into the total students equation:
\[ n = (120 - x) + x \]
Simplifying this gives:
\[ n = 120 \]

4. **Step 4: Conclusion.**
Therefore, the total number of students in the school is:
\[ n = 120 \]

### Final Answer:
The total number of students in the school is **120**.