In a survey of 450 people, it was found that 110 play cricket, 160 play tennis and 70 play both cricket as well as tennis. How many play neither cricket nor tennis?

Answer

To solve the problem step by step, we can use the principle of inclusion-exclusion to determine how many people play neither cricket nor tennis.

### Step-by-Step Solution:

1. **Identify the Total Number of People**:
We know from the problem that the total number of people surveyed is 450.

2. **Identify the Number of People Playing Each Sport**:
- Let \( C \) be the number of people who play cricket. \( C = 110 \)
- Let \( T \) be the number of people who play tennis. \( T = 160 \)
- Let \( B \) be the number of people who play both cricket and tennis. \( B = 70 \)

3. **Use the Inclusion-Exclusion Principle**:
To find the total number of people who play either cricket or tennis (or both), we can use the formula:
\[ \text{Number of people playing cricket or tennis} = C + T - B \]
Substituting the values:
\[ \text{Number of people playing cricket or tennis} = 110 + 160 - 70 \]

4. **Calculate the Total**:
\[ = 110 + 160 - 70 = 200 \]
So, 200 people play either cricket or tennis or both.

5. **Determine the Number of People Playing Neither Sport**:
To find the number of people who play neither cricket nor tennis, we subtract the number of people who play either sport from the total number of people surveyed:
\[ \text{Number of people playing neither} = \text{Total number of people} - \text{Number of people playing cricket or tennis} \]
Substituting the values:
\[ \text{Number of people playing neither} = 450 - 200 \]

6. **Final Calculation**:
\[ = 450 - 200 = 250 \]
Therefore, 250 people play neither cricket nor tennis.

### Final Answer:
**250 people play neither cricket nor tennis.**