If the difference between the average of $x, y$ and $y, z$ is $12,$ then the difference between $x$ and $z$ is

The average marks of a group of $20$ students on a test is reduced by $4$ when the topper who scored $90$ marks is replaced by a new student. Find the marks of the new student.

The average of a non-zero number and its square is $5$ times the number. The number is

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 $b > c$)

The average age of mother,father,and son was $42$ years at the time of the son's marriage. After one year,an infant was born in the family,and after $6$ years of marriage,the average age of the family is $36$ years. What was the age of the bride at the time of marriage in years?

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