Question

Mother is 25 year older than her son. Find son's age if after 8 years ratio of son's age to mother's age will be $\frac{4}{9}$.

Answer 1

Let the present age of the son be x years.

Age of the mother = (x + 25) years

After 8 years,
Age of son = (x + 8) years
Age of mother = (x + 25+ 8) years
= (x + 33) years

From the given information,
$$\begin{gathered} \frac{x+8}{x+33}=\frac{4}{9} \\ \therefore 9\left(x+8\right)=4\left(x+33\right) \\ \therefore 9x+72=4x+132 \\ \therefore 9x-4x=132-72 \\ \therefore 5x=60 \\ \therefore x=12 \end{gathered}$$

Hence, the present age of the son is 12 years.