If the present age of $X$ is half that of $Y$ and after $20$ years the age of $Y$ will be $1 \frac{1}{2}$ times that of $X$,what is the present age of $X$?

The sum of the ages of a father and son is $45$ years. $5$ years ago,the product of their ages was four times the father's age at that time. The present age of the father is (in years):

The ratio of the ages of $Ram$ and $Rahim, 10$ years ago was $1:3$. The ratio of their ages $5$ years hence will be $2:3$. Then the ratio of their present ages is:

In a family,a couple has a son and a daughter. The age of the father is three times that of his daughter and the age of the son is half of his mother. The wife is $9$ years younger than her husband and the brother is $7$ years older than his sister. What is the age of the mother? (in years)

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