The average age of a family of $6$ members is $22 \text{ years}$. If the age of the youngest member is $7 \text{ years}$,then what was the average age of the family at the birth of the youngest member?

The average weight of $36$ students is $50 \,kg$. It was found later that the weight of one of the students was misread as $73 \,kg$,whereas his actual weight was $37 \,kg$. Find the correct average (in $kg$).

The average of five numbers is $6.9$. If one of the numbers is deleted,the average of the remaining numbers is $4.4$. What is the value of the number deleted?

$A$ cricketer gives $12.4$ runs per wicket. He gives $26$ runs and takes $5$ wickets in a match,after which his average becomes $12$ runs per wicket. How many wickets had been taken till the last match?

Ten years ago,the average age of $P$ and $Q$ was $20 \text{ years}$. The average age of $P, Q,$ and $R$ is $30 \text{ years}$ now. After $10 \text{ years}$,the age of $R$ will be (in $\text{years}$):

$10$ years ago,the average age of all $25$ teachers of a girls' college was $45$ years. $4$ years ago,the principal retired at the age of $60$ years. One year later,a new principal aged $54$ years was recruited. Considering the principal as a teacher,what is the present average age of all $25$ teachers?