Question

The son is now 20 years younger than his father, and ten years ago he was three times younger than his father. How old are each of them now?

Answer 1

see a solution process below;

Explanation:

Let `x` represent the father's age..

Let `y` represent the son's age..

First Statement

`y = x - 20`

`x - y = 20 - - - eqn1`

Second Statement

`(y - 10) = (x - 10)/3`

`3(y - 10) = x - 10`

`3y - 30 = x - 10`

`3y - x = -10 + 30`

`3y - x = 20 - - - eqn2`

Solving simultaneously..

`x - y = 20 - - - eqn1`

`3y - x = 20 - - - eqn2`

Adding both equations..

`2y = 40`

`y = 40/2`

`y = 20`

Subsitute the value of `y` into `eqn1`

`x - y = 20 - - - eqn1`

`x - 20 = 20`

`x = 20 + 20`

`x = 40`

Hence the father's age `x = 40yrs`

and the son's age `y = 20yrs`