The ratio between the present ages of $P$ and $Q$ is $5: 7$. If the difference between $Q$'s present age and $P$'s age after $6$ $years$ is $2$,what is the sum of ages of $P$ and $Q$ at present? (in $years$)

The ratio of the present ages of $A$ and $B$ is $7:9$. $6$ years ago,the ratio of $\frac{1}{3}$ of $A$'s age at that time and $\frac{1}{3}$ of $B$'s age at that time was $1:2$. What will be the ratio of $A$'s to $B$'s age $6$ years from now?

Eighteen $years$ ago,the ratio of $A$'s age to $B$'s age was $8: 13$. Their present ages are in the ratio $5: 7$. What is the present age of $A$ (in $years$)?

The ratio between the present ages of $P$ and $Q$ is $6:7$. If $Q$ is $4 \text{ years}$ older than $P$,what will be the ratio of the ages of $P$ and $Q$ after $4 \text{ years}$?

The average age of $30$ students of a class is $14$ years $4$ months. After the admission of $5$ new students,the average age becomes $13$ years $9$ months. The youngest of the five new students is $9$ years $11$ months old. What is the average age of the remaining $4$ new students?

The ratio of the present ages of Anju and Sandhya is $13: 17$. $4$ years ago,the ratio of their ages was $11: 15$. What will be the ratio of their ages $6$ years hence?