$A$ cricketer,whose bowling average was $12.4$ runs/wicket,takes $5$ wickets for $22$ runs in a match,thereby decreasing his average by $0.4$. The number of wickets taken by him before this match was:

The average weight of $24$ students in section $A$ of a class is $58 \,kg,$ whereas the average weight of $26$ students in section $B$ of the same class is $60.5 \,kg$. Find out the average weight of all the $50$ students of the class. (in $kg$)

$A$ cyclist goes from one place to another and returns by the same route. He pedals his way uniformly with speed $u$ while going and with speed $v$ while returning. The average speed of his journey is

Five years ago,the average age of $P$ and $Q$ was $15 \text{ years}$. Now,the average age of $P$,$Q$,and $R$ is $20 \text{ years}$. What will be the age of $R$ after $10 \text{ years}$?

The mean of $11$ numbers is $35$. If the mean of the first $6$ numbers is $32$ and that of the last $6$ numbers is $37$, then find the sixth number.

The average age of $8$ members of a group is $40 \text{ years}$. The age of $1$ member is $55 \text{ years}$. After his retirement,a new member of age $39 \text{ years}$ joins the group. What is the effect of this replacement on the average age of the group?