Present ages of $X$ and $Y$ are in the ratio $5:6$. Seven years hence the ratio will become $6:7$. What is the present age of $X$ in years?

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?

$3 \text{ years}$ ago,the average age of a family of $5$ members was $17 \text{ years}$. $A$ baby having been born,the average age of the family is the same today. What is the age of the child? (in $\text{years}$)

The ratio between the present age of Manisha and Deepali is $5:x$. Manisha is $9$ years younger than Parineeta. Parineeta's age after $9$ years will be $33$ years. The difference between Deepali's and Manisha's age is the same as the present age of Parineeta. What will come in place of $x$?

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?

One $year$ ago,a father was four times as old as his son. In $6$ $years$ time,his age will exceed twice his son's age by $9$ $years$. The ratio of their present ages is: