The ratio of the present ages of $A$ and $B$ is $7:9$. $6$ years ago,the ratio of $\frac{1}{3}$ of $A$'s age at that time and $\frac{1}{3}$ of $B$'s age at that time was $1:2$. What will be the ratio of $A$'s to $B$'s age $6$ years from now?

$A$ father's age is three times the sum of the ages of his two children,but $20 \, \text{years}$ hence his age will be equal to the sum of their ages. Then,the father's age is (in $\text{years}$)

Ratio of the ages of Tania and Rakesh is $9:10$. $10 \text{ years}$ ago,the ratio of their ages was $4:5$. What is the present age of Rakesh (in $\text{years}$)?

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 $X$?

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 between the school ages of Neelam and Shaan is $5:6$. If the ratio between one-third of Neelam's age and half of Shaan's age is $5:9$,then what is the school age of Shaan (in years)?