The average age of a husband, his wife and their child $4$ years ago was $30\text{years}$. The average age of the wife and the child $6$ years ago was $22\text{years}$. Find the present age of the husband.

Let the present ages of the husband, wife, and child be $H$, $W$, and $C$ respectively.
Given:
The average age of $H$, $W$, and $C$, $4$ years ago was $30\text{years}$.

$$\frac{(H-4)+(W-4)+(C-4)}{3}=30$$

$$(H+W+C)-12=90$$

$$H+W+C=90+12=102\text{years}$$

Also given:
The average age of the wife and child, $6$ years ago was $22\text{years}$.

$$\frac{(W-6)+(C-6)}{2}=22$$

$$(W+C)-12=44$$

$$W+C=44+12=56\text{years}$$

To find the present age of the husband ($H$), substitute the value of $(W+C)$ into the first equation:

$$H+56=102$$

$$H=102-56=46\text{years}$$

Thus, the present age of the husband is $46\text{years}$.