25 people for programme A, 50 people for programme B, 10 people for both. So, number of employee employed only A is

Options

A. 15
B. 20
C. 35
D. 40

Explanation

To find the number of employees employed only in programme A, we can use the principle of set theory. Let's denote:

- \( N(A) \): the number of people in programme A = 25
- \( N(B) \): the number of people in programme B = 50
- \( N(A \cap B) \): the number of people in both programmes = 10

We need to find the number of people employed only in programme A, denoted as \( N(A \text{ only}) \).

### Step-by-Step Solution:

1. **Identify the total number of people in programme A**:
\[ N(A) = 25 \]
This means there are 25 people involved in programme A.

2. **Identify the number of people involved in both programmes**:
\[ N(A \cap B) = 10 \]
This means 10 people are counted in both programme A and programme B.

3. **Calculate the number of people employed only in programme A**:
To find the number of people employed only in programme A, we subtract the number of people involved in both programmes from the total number of people in programme A:
\[ N(A \text{ only}) = N(A) - N(A \cap B) \]
Substituting the values:
\[ N(A \text{ only}) = 25 - 10 = 15 \]

4. **Conclusion**:
Therefore, the number of employees employed only in programme A is:
\[ \boxed{15} \]