The average weight of $8$ persons increases by $2.5\, kg$ when a new person comes in place of one of them weighing $65\, kg$. What is the weight of the new person? (in $kg$)

The average weight of $10$ students is increased by $0.5 \, kg$ when one of the students weighing $50 \, kg$ is replaced by a new student. Find the weight of the new student (in $kg$).

$A$ club has $15$ men and $25$ women. The average age of men is $10 \text{ years}$ and the average age of women is $12 \text{ years}$. What is the average age of the whole club in years?

There were $35$ students in a hostel. If the number of students increases by $7$,the expenses of the mess increase by $Rs. 42$ per day,while the average expenditure per head diminishes by $Rs. 1$. Find the actual expenditure of the mess (in $Rs.$).

The average of ten numbers is calculated. If each number is increased by $12 \%$,then the average

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?