The age of a man 10 years ago was thrice the age of his son. 10 years hence, the man's age will be twice the age of his son. The ratio of their present ages is = ?

Let son's age 10 years ago be x years,
Then man's age 10 years ago = 3x years
Son's present age = (x + 10) years ,
Man's present age = (3x + 10) years
$$\eqalign{ & \left( {3x + 10} \right) + 10 = 2\left( {x + 10 + 10} \right) \cr & \Rightarrow 3x + 20 = 2\left( {x + 20} \right) \cr & \Rightarrow 3x + 20 = 2x + 40 \cr & \Rightarrow x = 20 \cr} $$
Ratio of present ages of man and the son
$$\eqalign{ & {\text{ = }}\frac{{3x + 10}}{{x + 10}} \cr & = \frac{{3 \times 20 + 10}}{{20 + 10}} \cr & = \frac{{70}}{{30}} \cr & = 7:3 \cr} $$