The average age of all the employees in an office is 42 years. 60% of the employees are males and the rest are females, The ratio of the average age of males to that of females is 6:5. What is the average age (in years) of male employees?

Options

A. 45
B. 40
C. `42.5`
D. `37.5`

Answer

To find the average age of male employees, we can follow these steps:

### Step 1: Understand the given information
- Average age of all employees = 42 years
- Percentage of male employees = 60%
- Percentage of female employees = 40%
- Ratio of average age of males to females = 6:5

### Step 2: Assume the total number of employees
Let's assume the total number of employees is 100. This makes calculations easier.
- Number of male employees = 60% of 100 = 60
- Number of female employees = 40% of 100 = 40

### Step 3: Set up the average age equation
Let the average age of male employees be \( M \) and the average age of female employees be \( F \). According to the ratio given:
\[ \frac{M}{F} = \frac{6}{5} \]
This implies:
\[ M = \frac{6}{5}F \]

### Step 4: Calculate total age of all employees
The total average age of all employees can be expressed as:
\[ \text{Total age of all employees} = \text{Average age} \times \text{Total number of employees} = 42 \times 100 = 4200 \]

### Step 5: Express total age in terms of \( M \) and \( F \)
The total age of male employees can be expressed as:
\[ \text{Total age of males} = M \times 60 \]
The total age of female employees can be expressed as:
\[ \text{Total age of females} = F \times 40 \]
Thus, the total age of all employees can also be expressed as:
\[ M \times 60 + F \times 40 = 4200 \]

### Step 6: Substitute \( M \) in the total age equation
Substituting \( M = \frac{6}{5}F \) into the total age equation:
\[ \left(\frac{6}{5}F\right) \times 60 + F \times 40 = 4200 \]
This simplifies to:
\[ \frac{360}{5}F + 40F = 4200 \]
\[ 72F + 40F = 4200 \]
\[ 112F = 4200 \]
\[ F = \frac{4200}{112} = 37.5 \]

### Step 7: Calculate \( M \)
Now that we have \( F \), we can find \( M \):
\[ M = \frac{6}{5}F = \frac{6}{5} \times 37.5 = 45 \]

### Final Answer
The average age of male employees is **45 years**.

---