The arithmetic mean of $100$ observations is $24$. If $6$ is added to each of the observations and then each of them is multiplied by $2.5$,find the new arithmetic mean.

In a class,the average height of all students is $a \text{ cm}$. Among them,the average height of $10$ students is $b \text{ cm}$ and the average height of the remaining students is $c \text{ cm}$. Find the number of students in the class. (Here $a > c$ and $b > c$)

$A$ class has $20$ boys and $30$ girls. The average age of boys is $11$ years and that of girls is $12$ years. What is the average age of the whole class in years?

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 average of the first nine prime numbers is:

The average of marks obtained by $120$ candidates in a certain examination is $35$. If the average marks obtained by passed candidates are $39$ and those of the failed candidates are $15$,then what is the number of candidates who passed the examination?