The average age of $35$ students in a class is $16$ years. The average age of $21$ students is $14$ years. What is the average age of the remaining $14$ students (in years)?

Three $years$ ago,the average age of a family of $5$ members was $17$ $years$. With the birth of a new baby,the average age of the family remains the same even today. Find the age of the baby (in $years$).

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 average monthly income of $P$ and $Q$ is $Rs. 5050$. The average monthly income of $Q$ and $R$ is $Rs. 6250$ and the average monthly income of $P$ and $R$ is $Rs. 5200$. The monthly income of $P$ is

The mean of the marks obtained by $100$ students is $60$. If the marks obtained by one of the students was incorrectly calculated as $75$ whereas the actual marks obtained by him were $65$,what is the correct mean of the marks obtained by the students?

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 of the teacher (in $kg$).