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

$A$ professional institute's total expenditure on students for a particular course is partly fixed and partly varies linearly with the number of students. The average expense per student is $Rs.\,615$ when there are $24$ students and $Rs.\,465$ when there are $40$ students. What is the average expense when there are $60$ students? (in $Rs.$)

The average age of $80$ boys in a class is $15.$ The average age of a group of $15$ boys in the class is $16$ and the average age of another $25$ boys in the class is $14.$ What is the average age of the remaining boys in the class?

The average age of $36$ students in a group is $14$ years. When the teacher's age is included, the average increases by $1$. What is the teacher's age in years?

If the average marks of three batches of $55, 60,$ and $45$ students are $50, 55,$ and $60$ respectively,then the average marks of all the students is:

The mean weight of $34$ students of a school is $42\, kg$. If the weight of the teacher is included, the mean weight increases by $400\, g$. Find the weight (in $kg$) of the teacher.