In a class of 60 students , 25 students play cricket and 20 students play tennis and 10 students play both the games. Find the number of students who play neither.

Options

A. 25
B. 35
C. 40
D. 15

Explanation

To solve the problem, we need to find out how many students play neither cricket nor tennis. We will use the principle of inclusion-exclusion to find the number of students who play at least one of the two games.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Total number of students in the class (N) = 60
- Number of students who play cricket (|C|) = 25
- Number of students who play tennis (|T|) = 20
- Number of students who play both games (|C ∩ T|) = 10

2. **Use the Inclusion-Exclusion Principle:**
The formula for the number of students who play either cricket or tennis (|C ∪ T|) is given by:
\[ |C ∪ T| = |C| + |T| - |C ∩ T| \]

3. **Substitute the Values:**
\[ |C ∪ T| = 25 + 20 - 10 \]

4. **Calculate |C ∪ T|:**
\[ |C ∪ T| = 35 \]
This means 35 students play either cricket or tennis.

5. **Find the Number of Students Who Play Neither:**
To find the number of students who play neither game, we subtract the number of students who play at least one game from the total number of students:
\[ \text{Number of students who play neither} = N - |C ∪ T| \]
\[ \text{Number of students who play neither} = 60 - 35 \]

6. **Calculate the Final Answer:**
\[ \text{Number of students who play neither} = 25 \]

### Final Answer:
The number of students who play neither cricket nor tennis is **25**.