The average weight of a class of $24$ students is $35 \, kg$. If the weight of the teacher is included, the average weight increases by $400 \, g$. The weight of the teacher is (in $kg$):

$A$ batsman scores $87$ runs in the $21^{st}$ match of his career. His average runs per match increase by $2.$ What is his average before the $21^{st}$ match?

The average of four consecutive odd numbers is $40$. What is the largest number?

The average age of a committee of $8$ members is $40 \text{ years}$. $A$ member,aged $55 \text{ years}$,retired and was replaced by a member aged $39 \text{ years}$. The average age of the present committee is (in $\text{years}$):

In a school, the average age of students is $6 \, \text{years}$, and the average age of $12$ teachers is $40 \, \text{years}$. If the average age of the combined group of all the teachers and students is $7 \, \text{years}$, then the number of students is?

The average marks of $40$ students in an English exam is $72$. Later,it is found that three marks $64, 62,$ and $84$ were wrongly entered as $68, 65,$ and $73$. The average after the mistakes were rectified is: