In a cricket team of $11$ boys, one player weighing $42 \,kg$ is injured and replaced by another player. If the average weight of the team is increased by $100\, gm$ as a result of this, then what is the weight of the new player? (in $kg$)

$10$ $years$ ago the average age of all the $25$ $teachers$ of the Girls college was $45\, years.$ $4 \,years$ ago, the principal has retired from her post at the age of $60 \,year.$ So after one year a new principal whose age was $54 \,years$ recruited from outside. The present average age of all the teachers is, if principal is also considered as a teacher

The average weight of a class of $24$ students is $35 \,kg$. If the weight of the teacher is included the average rises by $400\, g.$ The weight of the teacher is (in $kg$)

The mean of $19$ observations is $4 .$ If one more observation of $24$ is added to the data, the new mean will be

The average of $6$ numbers is $3.95.$ The average of two of them is $3.4,$ while the average of the other two is $3.85 .$ What is the average of the remaining two numbers ?