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 $b > c$)

In a set of prime and composite numbers,the number of composite numbers is twice the number of prime numbers,and the average of all the numbers in the set is $9$. If the number of prime numbers and composite numbers are exchanged,then the average of the set of numbers increases by $2$. If,during the exchange of the numbers,the average of the prime numbers and composite numbers individually remained constant,then what was the ratio of the average of composite numbers to the average of prime numbers (initially)?

In a class,the average height of $35$ girls was measured as $160 \,cm$. Later,it was discovered that the height of one of the girls was misread as $144 \,cm$,while her actual height was $104 \,cm$. What was the actual average height of the girls in the class? (in $cm$) (rounded off to two digits after decimal)

The average of runs of a cricket player of $10$ innings was $32$. How many runs must he score in his next innings so as to increase his average of runs by $4$?

$A$ batsman makes a score of $81$ runs in the $16^{\text{th}}$ match and thus increases his average runs per match by $3$. What is his average after the $16^{\text{th}}$ match?

If the average of $m$ numbers is $n^{2}$ and that of $n$ numbers is $m^{2},$ then the average of $(m + n)$ numbers is