In my office the average age of all the female employees is 21 years and that of male employees is 32 years, where the average age of all the (male and female) employees is 28 years. The total no. of employee in my office could be:

Options

A. 35
B. 78
C. 231
D. 90

Answer

To solve the problem, we will use the concept of alligation to find the total number of employees in the office based on the average ages provided.

### Step-by-Step Solution:

1. **Identify the Average Ages**:
- Average age of female employees (A_f) = 21 years
- Average age of male employees (A_m) = 32 years
- Overall average age of all employees (A_o) = 28 years

2. **Calculate the Differences**:
- Difference between the average age of females and the overall average:
\[ D_f = A_o - A_f = 28 - 21 = 7 \]
- Difference between the average age of males and the overall average:
\[ D_m = A_m - A_o = 32 - 28 = 4 \]

3. **Set Up the Ratio**:
- The ratio of the number of female employees (N_f) to male employees (N_m) can be represented as:
\[ \frac{N_f}{N_m} = \frac{D_m}{D_f} = \frac{4}{7} \]

4. **Express Total Employees**:
- Let the number of male employees be \( 4x \) and the number of female employees be \( 7x \).
- Therefore, the total number of employees (N) can be expressed as:
\[ N = N_f + N_m = 7x + 4x = 11x \]

5. **Determine Possible Values for Total Employees**:
- The total number of employees must be a multiple of 11. We need to check the options provided to see which one is a multiple of 11.

6. **Check the Options**:
- Given options: 35, 48, 231, 9
- Checking each:
- 35 is not a multiple of 11.
- 48 is not a multiple of 11.
- 231 is a multiple of 11 (since \( 231 \div 11 = 21 \)).
- 9 is not a multiple of 11.

7. **Conclusion**:
- The total number of employees in the office could be **231**.