Question

A man's age is $30$ years more than the age of his son. If the sum of their ages is $56$ years, find the age of the son.

Answer 1

Let the age of son be $x$ and that of his father be $y$.

According to the question, we have

$y=x+30$ [$\because$ Father is $30$ years older then his son ]

$\Rightarrow y-x=30$.....(i)

and $x+y=56$ ....(ii) [Sum of their ages is $56$]

Adding equation(i) and (ii), we have

$\Rightarrow y-x+x+y=30+56$

$\Rightarrow 2y=86$

$\Rightarrow y=43$

Substitute $y=43$ in equation (i), we get

$y=x+30$

$43-30=x$

$\therefore x=13$

Hence, son's age$=13$years.