According to the stock policy of a company , each employee in the technical division only is given 15 shares of the company and each empolyee in the recrutiment division only is given 10 shares. Employees belonging to both communities get 25 share each. There are 20 employees in the company, and each one belong to at least one division. The cost of each share is $10. If the technical division has 15 employees and the recruitment division has 10 employees, then what is the total cost of the shares gives by the company?

Options

A. 2250
B. 2650
C. 3120
D. 3250

Answer

To solve the problem step by step, we will follow the information given in the question and apply some basic set theory.

### Step 1: Understand the given information
- Total employees in the company = 20
- Employees in the Technical division = 15
- Employees in the Recruitment division = 10
- Employees in both divisions = ?
- Each employee in the Technical division gets 15 shares.
- Each employee in the Recruitment division gets 10 shares.
- Employees in both divisions get 25 shares.
- Cost of each share = $10

### Step 2: Set up the equation using set theory
Let:
- \( A \) = set of employees in the Technical division
- \( B \) = set of employees in the Recruitment division

Using the principle of inclusion-exclusion for sets, we have:
\[ N(A \cup B) = N(A) + N(B) - N(A \cap B) \]
Where:
- \( N(A \cup B) \) = total number of employees = 20
- \( N(A) \) = number of employees in Technical division = 15
- \( N(B) \) = number of employees in Recruitment division = 10
- \( N(A \cap B) \) = number of employees in both divisions (let's denote this as \( x \))

Substituting the known values into the equation:
\[ 20 = 15 + 10 - x \]
This simplifies to:
\[ 20 = 25 - x \]
Rearranging gives:
\[ x = 25 - 20 = 5 \]
So, \( N(A \cap B) = 5 \).

### Step 3: Calculate the number of employees in only one division
- Employees only in Technical division = \( N(A) - N(A \cap B) = 15 - 5 = 10 \)
- Employees only in Recruitment division = \( N(B) - N(A \cap B) = 10 - 5 = 5 \)

### Step 4: Calculate the total shares distributed
1. **Shares given to employees only in Technical division**:
\[ \text{Shares} = 10 \text{ employees} \times 15 \text{ shares/employee} = 150 \text{ shares} \]

2. **Shares given to employees only in Recruitment division**:
\[ \text{Shares} = 5 \text{ employees} \times 10 \text{ shares/employee} = 50 \text{ shares} \]

3. **Shares given to employees in both divisions**:
\[ \text{Shares} = 5 \text{ employees} \times 25 \text{ shares/employee} = 125 \text{ shares} \]

### Step 5: Calculate total shares
\[ \text{Total shares} = 150 + 50 + 125 = 325 \text{ shares} \]

### Step 6: Calculate the total cost of the shares
\[ \text{Total cost} = \text{Total shares} \times \text{Cost per share} = 325 \times 10 = 3250 \]

### Final Answer
The total cost of the shares given by the company is **$3250**.

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