The average weight of $6$ persons is increased by $5\, kg$ when one of them who weighs $40\, kg$ is replaced by a new man. The weight of new man is (in $kg$)

$A , B , C , D\, \& \,E$ are five consecutive even numbers. Average of $A$ and $E$ is $46 .$ What is the largest number?

What is the age of a class teacher?

$I.$ There are $11$ students in the class.

$II.$ The average age of the students and the teacher is $14$ years.

$III.$ The average age of the teacher and the students is $3$ years more than that of the students.

The arithmetic mean of $100$ observations is $24.6$ is added to each of the observations and, then each of them is multiplied by $2.5 .$ Find the new arithmetic mean.

The average marks obtained by $40$ students of a class is $86 .$ If the $5$ highest marks are removed, the average reduces by one mark. The average marks of the top $5$ students is