The average of first three numbers is double of the fourth number. If the average of all the four numbers is $12,$ find the $4^{th}$ number.

Last year,$5$ companies had an average of $16$ non-working days each. If $3$ companies had $16$ non-working days each and $2$ companies had $5$ fewer non-working days each,what was the average number of non-working days for these $5$ companies last year?

The average of six numbers is $32$. If each of the first three numbers is increased by $2$ and each of the remaining three numbers is decreased by $4$,then the new average is?

In the first $30$ overs of a cricket match,the run rate was $5.2 \text{ runs/over}$. What is the required run rate in the remaining $20$ overs to reach the target of $280$ runs?

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