A group of 30 employees of Cadre A has a mean age of 27. A different group of 70 employees of Cadre B has a mean age of 23. What is the mean age of the employees of the two group togeters?

Options

A. 23
B. 24.2
C. 25
D. 26.8

Answer

To find the mean age of the employees of Cadre A and Cadre B together, we can follow these steps:

### Step 1: Calculate the total sum of ages for Cadre A
Given:
- Number of employees in Cadre A = 30
- Mean age of Cadre A = 27

The formula for the sum of ages is:
\[ \text{Sum of A} = \text{Mean Age} \times \text{Number of Employees} \]

Calculating:
\[ \text{Sum of A} = 27 \times 30 = 810 \]

### Step 2: Calculate the total sum of ages for Cadre B
Given:
- Number of employees in Cadre B = 70
- Mean age of Cadre B = 23

Using the same formula:
\[ \text{Sum of B} = \text{Mean Age} \times \text{Number of Employees} \]

Calculating:
\[ \text{Sum of B} = 23 \times 70 = 1610 \]

### Step 3: Calculate the total sum of ages for both Cadres
Now, we can find the total sum of ages for both groups:
\[ \text{Total Sum} = \text{Sum of A} + \text{Sum of B} \]
\[ \text{Total Sum} = 810 + 1610 = 2420 \]

### Step 4: Calculate the total number of employees
The total number of employees from both Cadres is:
\[ \text{Total Employees} = \text{Number of Employees in A} + \text{Number of Employees in B} \]
\[ \text{Total Employees} = 30 + 70 = 100 \]

### Step 5: Calculate the mean age of the combined groups
Now we can find the mean age of the two groups together:
\[ \text{Mean Age} = \frac{\text{Total Sum}}{\text{Total Employees}} \]
\[ \text{Mean Age} = \frac{2420}{100} = 24.2 \]

### Final Answer:
The mean age of the employees of the two groups together is **24.2**.

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