The average of $17$ numbers is $10.9$. If the average of the first $9$ numbers is $10.5$ and the average of the last $9$ numbers is $11.4$, find the middle number.

$A$ person covers $9 \, km$ with a speed of $3 \, km/h$,$25 \, km$ with a speed of $5 \, km/h$,and $30 \, km$ with a speed of $10 \, km/h$. Find the average speed of the person in $km/h$.

Eleven years earlier,the average age of a family of $4$ members was $28 \, \text{years}$. Now,the average age of the same family with $6$ members is still the same,even though $2$ children were born in this period. If they belong to the same parents and the age of the first child at the time of the birth of the younger child was the same as the total number of family members just after the birth of the youngest member,then what is the present age of the youngest member of the family in years?

The average salary per head of all workers of an institution is $Rs. 60$. The average salary per head of $12$ officers is $Rs. 400$. The average salary per head of the rest is $Rs. 56$. Then,the total number of workers in the institution is?

The average age of four brothers is $12 \, \text{years}$. If the age of their mother is also included, the average increases by $5 \, \text{years}$. The age of the mother (in $\text{years}$) is:

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.