Question

The sum of the ages of a father and his son is $48$ years. Six years ago, the father's age was five times the age of his son. Find their present ages.

• A. Present age of Father is $30$ years and
  Present age of son is $10$ years
• B. Present age of Father is $48$ years and
  Present age of son is $16$ years
• C. Present age of Father is $45$ years and
  Present age of son is $15$ years
• D. Present age of Father is $36$ years and
  Present age of son is $12$ years

Answer 1

The correct option is D Present age of Father is $36$ years and

Present age of son is $12$ years

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

It is given that the sum of the ages of a father and his son is $48$ years that is:

$x+y=\mathrm{48..........}\left(1\right)$

Also, six years ago, the father's age was five times the age of his son that is:

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

$x-6=5y-30$

$x-5y=-30+6$

$x-5y=-\mathrm{24..........}\left(2\right)$

Now subtract equation 1 from equation 2 to eliminate $x$, because the coefficients of $x$ are same. So, we get

$(x-x)+(-5y-y)=-24-48$

i.e. $-6y=-72$

i.e. $y=12$

Substituting this value of $y$ in (1), we get

$x+12=48$

i.e. $x=48-12=36$

Hence, the present age of the father is $36$ years and the present age of the son is$12$ years.