In a group of 100 persons 85 take tea 20 take coffee and 25 take tea and coffee . Number of persons who take neither tea nor coffee is

Options

A. 5
B. 15
C. 25
D. 20

Answer

To solve the problem, we need to find the number of persons who take neither tea nor coffee. We can use the principle of inclusion-exclusion to find this.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Total number of persons (N) = 100
- Number of persons who take tea (N(T)) = 85
- Number of persons who take coffee (N(C)) = 20
- Number of persons who take both tea and coffee (N(T ∩ C)) = 25

2. **Use the Inclusion-Exclusion Principle:**
We need to find the number of persons who take either tea or coffee or both, which is represented as N(T ∪ C). The formula for this is:
\[ N(T ∪ C) = N(T) + N(C) - N(T ∩ C) \]

3. **Substitute the Values:**
\[ N(T ∪ C) = 85 + 20 - 25 \]

4. **Calculate N(T ∪ C):**
\[ N(T ∪ C) = 85 + 20 - 25 = 80 \]

5. **Find the Number of Persons Who Take Neither Tea Nor Coffee:**
To find the number of persons who take neither tea nor coffee, we subtract the number of persons who take either or both from the total number of persons:
\[ \text{Number of persons who take neither} = N - N(T ∪ C) \]
\[ \text{Number of persons who take neither} = 100 - 80 = 20 \]

### Final Answer:
The number of persons who take neither tea nor coffee is **20**.

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