Question

The sum of the present ages of the father and his son is $45$ years. $5$ years ago, the age of the father was $6$ times that of son. What is the present age of the son ?

Answer 1

Let the present age of the father is $x$ years and the present age of his son is $y$ years.

Sum of their present age $=x+y=45$ ............ (1)

$5$ years ago, age of the father $=x-5$ years

$5$ years ago, age of his son $=y-5$ years

$5$ years ago, the age of the father was $6$ times that of son.

So,

$x-5=6(y-5)$

$x-5=6y-30$

$6y-x=-5+30$

$6y-x=25$ ............. (2)

Add equation (1) and (2),

$x+y+6y-x=45+25$

$7y=70$

$y=10$ years

So, the present age of the son is $10$ years.