The sum of the numerator and denominator of a fraction is $12$. If the denominator is increased by $3,$ then the fraction becomes $\frac{1}{2}$. Find the fraction.

The denominator of a fraction is $4$ more than twice the numerator. When both the numerator and denominator are decreased by $6$, then the denominator becomes $12$ times the numerator. Determine the fraction.

A fraction is such that if the numerator is multiplied by $3$ and the denominator is reduced by $3$, we get $\frac{18}{11}$, but if the numerator is increased by $8$ and the denominator is doubled, we get $\frac{2}{5}$. Find the fraction.

The sum of numerator and denominator of a fraction is $3$ less than twice the denominator. If the numerator and denominator are increased by $1$, the numerator becomes half the denominator. Find the fraction.

Six years hence a man's age will be three times the age of his son and three years ago he was nine times as old as his son. Find their present ages.