Question

A father's present age is seven years less than $30$ times of what his son's age was $20$ years ago. Also, the father's present age is $31$ years more than his won's present age. Find the sum of their present ages in years.

Answer 1

Let the present age of father be $f$ years.
Let sons present age be $s$ years
Then, $f=30(s-20)-7$ .....(1);
and $f=s+31$ .....(2)

Equate (1) and (2), we get
$s+31=30s-600-7$

$\Rightarrow 638=29s$

$\Rightarrow 22=s$
$\Rightarrow f=53$

Thus, age of son is $22$ years and age of father is $53$ years.
Therefore, sum of their ages is $75$ years.