$A$ man is $3 \, \text{years}$ older than his wife and four times as old as his son. If the son becomes $15 \, \text{years}$ old after $3 \, \text{years}$, what is the present age of the wife? (in $\text{years}$)

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):

Radha's present age is three years less than twice her age $12$ years ago. Also,the ratio between Raj's present age and Radha's present age is $4:9$. What will be Raj's age after $5$ years? (in years)

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?

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)

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 $X$?