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 $kg$)

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 $years$).

The average of three numbers is $28$. If the first number is half of the second and the third number is twice the second,then the third number is?

The average age of a man and his two twin sons,born on the same day,is $30 \, \text{years}$. The ratio of the ages of the father and one son is $5:2$. What is the father's age in $\text{years}$?

Of the three numbers,the first is twice the second and the second is thrice the third. If the average of the three numbers is $10$,the numbers are

$10$ years ago,the average age of all $25$ teachers of a girls' college was $45$ years. $4$ years ago,the principal retired at the age of $60$ years. One year later,a new principal aged $54$ years was recruited. Considering the principal as a teacher,what is the present average age of all $25$ teachers?