The average weight of $24$ students is $35\, kgs.$ If the weight of teacher is added the average increased by $400\, gms$. What is the weight of the teacher? (in $kg$)

The average age of a group of $18$ persons is $32$ $years$ and $6 \,months.$ If two persons of age $65\, years$ each and one person of age $50\, years$ leave the group, the average age of the remaining persons in the group will be (in $years$)

The average weight of $10$ students is increased by half a $kg$ when one of the students weighing $50\, kg$ is replaced by a new student. Find out the weight of the new student.(in $kg$)

Three years ago, the average age of a family of $5$ members was $17\, years.$ A baby having been born, the average age of the family is the same today. The present age of the baby is (in $years$)

In a competitive examination, the average marks obtained was $45 .$ It was later discovered that there was some error in computerization and the marks of $90$ candidates had to be changed from $80$ to $50$ , and the average came down to $40$ marks. The total number of candidates appeared in the examination is