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?

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Answer 1 · 2018-03-30T00:11:08

see a solution process below;

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 $y = 20yrs$