The average age of $x$ and $y$ is $20$ years. If $z$ were to replace $x$,the average would be $19$ and if $z$ were to replace $y$,the average would be $21$. Find the ages of $x, y$ and $z$.

The average temperature for Monday,Tuesday,Wednesday and Thursday was $48^{\circ}$. The average temperature for Tuesday,Wednesday,Thursday and Friday was $52^{\circ}$. If the temperature on Monday was $42^{\circ}$,then the temperature on Friday was (in $degrees$):

The mean of marks secured by $50$ students in division $A$ of class $X$ is $61$,$25$ students of division $B$ is $57$,and that of $50$ students of division $C$ is $55$. What will be the mean of marks of the students of three divisions of Class $X$?

The average weight of $100$ students is $32\, kg$. The average weight of the first $49$ students is $30\, kg$ and that of the last $50$ students is $34\, kg$. What is the weight (in $kg$) of the $50^{th}$ student?

If the average of $6$ consecutive even numbers is $25,$ the difference between the largest and the smallest number is

In a coconut grove,$(x+2)$ trees yield $60$ nuts per year,$x$ trees yield $120$ nuts per year,and $(x-2)$ trees yield $180$ nuts per year. If the average yield per year per tree is $100$,find the value of $x$.