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 marks of a class of $35$ children is $35$. The marks of one of the students,who got $35$,was incorrectly entered as $65$. What is the correct average of the class?

The average weight of $25$ persons is increased by $1 \, kg$ when one man weighing $60 \, kg$ is replaced by a new person. What is the weight of the new person (in $kg$)?

$10$ years ago,the average age of a family of $4$ members was $24$ years. Two children have been born (with an age difference of $2$ years),and the present average age of the family remains the same. The present age of the youngest child is (in years):

The average weight of $21$ boys was recorded as $64 \, kg$. If the weight of the teacher was added,the average increased by $1 \, kg$. What was the teacher's weight (in $, kg$)?

The average of three consecutive odd numbers is $12$ more than one-third of the first of these numbers. What is the last of the three numbers?