Question :
"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 male and female employees is 28 years. The total number of employees in my office could be :"
Doubt:
I am completely unable to frame the question as to the given requirements. I understand that this should pertain to a certain multiple which we could be interested with.
On
Suppose we have $m$ male employees with ages $m_i$, and $f$ female employees with ages $f_i$. Then the question is saying
$$\frac 1 m \sum_{i=1}^m m_i = 32 \qquad \frac 1 f \sum_{i=1}^f f_i = 21 \qquad \frac{1}{m+f} \sum_{i=1}^{m+f} m_i + f_i = 28$$
and asking you to find $m+f$.
Notice that
$$\begin{align*} m+f &= \frac{1}{28} \left( \sum_{i=1}^m m_i + \sum_{i=1}^f f_i \right) \\ \sum_{i=1}^m m_i &= 32m \\ \sum_{i=1}^f f_i &= 21f \end{align*}$$
Hence
$$m+f = \frac{1}{28} \cdot 32m + \frac{1}{28} \cdot 21f$$
giving
$$ - \frac 1 7 m + \frac 1 4 f = 0 $$
So what are some positive-integer solutions to this equation?
From the given information, if the the number of female employees is $f$ and the number of male employees is $m$ then
$21 f + 32 m = 28 (f + m)$
From which,
$ 7 f - 4 m = 0 $
whose solution is
$ f = 4 k, m = 7 k $ where $k$ is an integer
Thus the total number of employees is $ f + m = 11 k $
That is, the total number of employees is a multiple of $11$.