Question

Five years ago, the age of a father was thrice the age of his son. In five years time, the age of the father will be twice the age of his son at that time. Find their present ages.

• A. Present age of father is $60$ years and present age of son is $20$ years
• B. Present age of father is $35$ years and present age of son is $15$ years
• C. Present age of father is $65$ years and present age of son is $25$ years
• D. Present age of father is $50$ years and present age of son is $15$ years

Answer 1

Answer: (B)

Present age of father is $35$ years and present age of son is $15$ years

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

It is given that five years ago, the age of a father was thrice the age of his son that is:

$x-5=3(y-5)$

$x-5=3y-15$

$x-3y=-15+5$

$x-3y=-\mathrm{10..........}\left(1\right)$

Also, in five years time, the age of the father will be twice the age of his son at that time that is:

$x+5=2(y+5)$

$x+5=2y+10$

$x-2y=10-5$

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

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

$(x-x)+(-2y+3y)=5+10$

i.e. $y=15$

Substituting this value of $y$ in (2), we get

$x-30=5$

i.e. $x=5+30=35$

Hence, the present age of the father is $35$ years and the present age of the son is$15$ years.