The average salary of all the workers in a workshop is $Rs. 8000$. The average salary of $7$ technicians is $Rs. 12000$ and the average salary of the rest is $Rs. 6000$. The total number of workers in the workshop is

$A$ student was asked to find the arithmetic mean of the numbers $3, 11, 7, 9, 15, 13, 8, 19, 17, 21, 14$ and $x$. He found the mean to be $12$. What should be the number in place of $x$?

$A$ batsman makes a score of $270$ runs in the $87^{th}$ inning and thus increases his average by a certain number of runs that is a whole number. Find the possible values of the new average.

The average weight of $8$ persons increases by $2.5\, kg$ when a new person comes in place of one of them weighing $65\, kg$. What is the weight of the new person? (in $kg$)

$A$ 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?

The average age of Donald,his wife,and their two children is $23 \text{ years}$. His wife is $4 \text{ years}$ younger than Donald,and his wife was $24 \text{ years}$ old when his daughter was born. He was $32 \text{ years}$ old when his son was born. What is the average age of Donald and his daughter? (in $\text{years}$)