Question

Two years ago, father was three times as old as his son and two years hence, twice his age will be equal to five times that of his son. Find their present ages.

Answer 1

Let the age of son $2$ years ago $=x$ years

Age of father $2$ years ago $=3x$ years

Now, the present age of son $=x+2$ years

the present age of father $=3x+2$ years

Now, After 2 years :

son's age $=x+4$ years

father's age $=3x+4$ years

Now, according to question, we have

$2(3x+4)=5(x+4)$ [Given: $2\times$ Father's age $=5\times$ (Son's age) ]

$\Rightarrow 6x+8=5x+20$

$\Rightarrow 6x-5x=20-8$

$\Rightarrow x=12$

Now, present age of son $=x+2=12+2=14$ years

And, the present age of father $=3x+2=3\times 12+2=38$ years