When I am as old my father is now, I shall be five times as old as my son is now. By then, my son will be $8$ years older than I am now. The combined age of my father and myself is $100$ years. How old is my son ?

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Solution

Let my son's age and my age be $x$ and $y$ , respectively.
Therefore, my father's age is $5 x$
$\Rightarrow 5 x + y = 100$ ....(i)
Number of years I will take to reach my father's age $= 5 x - 7$
In $(5 x - 7)$ years, my son's age will become
$x + 5 x - y = 6 x - y$
It is given that $6 x - y = y + 8$
$\Rightarrow 6 x - 2 y = 8$ ...........(ii)
Solving (i) and (ii) we get,
$x = 13$ years

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