Averages Questions

The average of v numbers is w
2
and that of w numbers is v
2
. Then the average of all the numbers is:

The average age of all the students of a class is 18 years. The average age of the boys of the class is 19 years and of the girls is 14 years. If the number of girls in the class is 30, then what is the number of boys in the class?

The captain of a cricket team of $11$ members is $29\text{ years}$ old, and the wicket-keeper is four years older than the captain. If the ages of the captain and the wicket-keeper are excluded, the average age of the remaining players of the team is two years less than the average age of the whole team. What is the average age of the team?

Refer to the data table below and answer the following question:Number of employeesAnnual salary (in lakhs)Bonus as percent of annual salaryManager$24$$8$ Executive$12$$8$ Trainee$14$$1$ What is the average bonus (in rupees)?

In the first $43$ overs of a cricket match, the run rate was $5\text{ runs/over}$. Calculate the required run rate in the remaining $7$ overs to reach the target of $285$ runs?