The average of six numbers is $32$. If each of the first three numbers is increased by $2$ and each of the remaining three numbers is decreased by $4$,then the new average is?

What is the average of all numbers between $8$ and $74$ which are divisible by $7\, ?$

The average of $10$ numbers is $7$. What will be the new average if each of the numbers is multiplied by $8$?

There are two groups $A$ and $B$ of a class,consisting of $42$ and $28$ students,respectively. If the average weight of group $A$ is $25 \, kg$ and that of group $B$ is $40 \, kg$,find the average weight of the whole class.

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.

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?