In a group of 50presons, everyone takes either tea of coffee. If 35 take tea and 25 take coffee, then the number of persons who take tea only (and not coffee) is

Options

A. 10
B. 25
C. 35
D. 30

Answer

To solve the problem, we need to determine the number of persons who take only tea and not coffee in a group of 50 people, where 35 take tea and 25 take coffee.

### Step-by-Step Solution:

1. **Identify the Total Number of People**:
- The total number of people in the group is given as 50.

2. **Identify the Number of Tea and Coffee Drinkers**:
- Number of people who take tea (N(T)) = 35
- Number of people who take coffee (N(C)) = 25

3. **Set Up the Equation for Total People**:
- Since everyone takes either tea or coffee, we can use the principle of inclusion-exclusion:
\[ N(T \cup C) = N(T) + N(C) - N(T \cap C) \]
Here, \(N(T \cup C)\) is the total number of people (50), \(N(T)\) is the number of tea drinkers, \(N(C)\) is the number of coffee drinkers, and \(N(T \cap C)\) is the number of people who drink both tea and coffee.

4. **Substitute the Known Values**:
- Plugging in the values we have:
\[ 50 = 35 + 25 - N(T \cap C) \]

5. **Solve for N(T ∩ C)**:
- Rearranging the equation gives:
\[ N(T \cap C) = 35 + 25 - 50 \]
\[ N(T \cap C) = 10 \]
This means that 10 people drink both tea and coffee.

6. **Calculate the Number of People Who Take Only Tea**:
- To find the number of people who take only tea (not coffee), we subtract the number of people who drink both from the total number of tea drinkers:
\[ N(\text{Only Tea}) = N(T) - N(T \cap C) \]
\[ N(\text{Only Tea}) = 35 - 10 = 25 \]

### Final Answer:
The number of persons who take only tea (and not coffee) is **25**.

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