The average age of $36$ students in a group is $14$ years. When the teacher's age is included, the average increases by $1$. What is the teacher's age in years?

In the first $10$ overs of a cricket game,the run rate was only $3.2$. What should be the run rate in the remaining $40$ overs to reach the target of $282$ runs?

The average weight of $A, B$ and $C$ is $45\, kg$. If the average weight of $A$ and $B$ is $40\, kg$ and that of $B$ and $C$ is $43\, kg$,then the weight of $B$ is (in $, kg$)

If the mean of $a, b, c$ is $M$ and $ab + bc + ca = 0$,then the mean of $a^2, b^2, c^2$ is

$A$ man covers $\frac{1}{3}$ of his journey by train at $80\, km/h$,the next $\frac{1}{3}$ by bus at $60\, km/h$,and the rest by bicycle at $30\, km/h$. Find the average speed of the man during the whole journey (in $km/h$).

The average age of a committee of $8$ members is $40 \text{ years}$. $A$ member,aged $55 \text{ years}$,retired and was replaced by a member aged $39 \text{ years}$. The average age of the present committee is (in $\text{years}$):