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 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 age of the father is $30 \text{ years}$ more than the son's age. Ten $\text{years}$ hence,the father's age will become three times the son's age at that time. What is the son's present age in $\text{years}$?

$Q$ is as much younger than $R$ as he is older than $T.$ If the sum of the ages of $R$ and $T$ is $60 \text{ years},$ what is definitely the difference between $R$ and $Q$'s age? (in $\text{years}$)

The average age of women and child workers in a factory was $15 \text{ years}$. The average age of all the $16$ children was $8 \text{ years}$ and the average age of women workers was $22 \text{ years}$. If $10$ women workers were married,then the number of unmarried women workers is: