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

Average age of $A, B$ and $C$ is $84 \text{ years}$. When $D$ joins them,the average age becomes $80 \text{ years}$. $A$ new person,$E$,whose age is $4 \text{ years}$ more than $D$,replaces $A$ and the average of $B, C, D$ and $E$ becomes $78 \text{ years}$. What is the age of $A$ (in $\text{years}$)?

The average of the first $7$ integers in a series of $13$ consecutive odd integers is $37$. What is the average of the entire series?

$3 \, \text{years}$ ago,the average age of a family of $5 \, \text{members}$ was $17 \, \text{years}$. With the birth of a new baby,the average age of the $6 \, \text{members}$ remains the same even today. Find the age of the new baby in years.

The average of three consecutive odd numbers is $12$ more than one-third of the first of these numbers. What is the last of the three numbers?

The average age of $5$ sisters is $20 \, \text{years}$. If the age of the youngest sister is $4 \, \text{years}$,what was the average age of the group of sisters at the time of the birth of the youngest sister?