If the average of $m$ numbers is $n^{2}$ and that of $n$ numbers is $m^{2}$,then the average of $(m + n)$ numbers is

The average age of a husband and wife,who were married $7 \, \text{years}$ ago,was $25 \, \text{years}$ at the time of their marriage. Now,the average age of the family,including the husband,wife,and a child born during the interval,is $22 \, \text{years}$. What is the present age of the child in $\text{years}$?

$A$ man retired from his service at the age of $60$. He served for $\frac{3}{5}$ of his retirement age. At what age (in $years$) did he join his job?

The sum of five numbers is $260$. The average of the first two numbers is $30$ and the average of the last two numbers is $70$. What is the third number?

The average of $X_{1}, X_{2}$ and $X_{3}$ is $14$. Twice the sum of $X_{2}$ and $X_{3}$ is $30$. What is the value of $X_{1}$?

The average weight of a group of $20$ boys was calculated to be $89.4 \text{ kg}$ and it was later discovered that one weight was misread as $78 \text{ kg}$ instead of the correct one of $87 \text{ kg}$. The correct average weight is in $\text{kg}$.