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 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 $kg$)

After replacing an old member with a new member,it was found that the average age of five members of a club is the same as it was $3 \, \text{years}$ ago. What is the difference between the ages of the replaced member and the new member (in $\text{years}$)?

The sum of three numbers is $98$. If the ratio between the first and second is $2:3$ and that between the second and the third is $5:8$,then the second number is

$A$ family consists of grandparents,parents,and three grandchildren. The average age of the grandparents is $67 \text{ years}$,that of the parents is $35 \text{ years}$,and that of the grandchildren is $6 \text{ years}$. What is the average age of the family? (in $\text{years}$)

The average salary of all the staff in an office of a corporate house is $Rs. 5,000$. The average salary of the officers is $Rs. 14,000$ and that of the rest is $Rs. 4,000$. If the total number of staff is $500$,what is the number of officers?