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?

$3 \text{ years}$ 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 of the present ages of two brothers is $1:2$ and $5 \text{ years}$ back,the ratio was $1:3$. What will be the ratio of their ages after $5 \text{ years}$?

Radha's present age is $3 \text{ years}$ less than twice her age $12 \text{ years}$ ago. Also,the ratio of Raj's present age to Radha's present age is $4:9$. What will be Raj's age after $5 \text{ years}$? (in $\text{years}$)

Ram's present age is three times his son's present age and $\frac{2}{5}$ of his father's present age. The average of the present ages of all of them is $46 \, \text{years}$. What is the difference between the Ram's son's present age and Ram's father's present age? (in $\text{years}$)

The ratio of $A$'s and $B$'s ages is $4:5.$ If the difference between the present age of $A$ and $B$'s age $5$ years hence is $3,$ then what is the sum of the present ages of $A$ and $B$ (in years)?