Question

The father's age is six times his son's age. Four years hence, the age of the father will be four times his son's age. The present ages, in years, of the son and the father are respectively,

• A. $4$ and $24$
• B. $5$ and $30$
• C. $6$ and $36$
• D. $3$ and $24$

Answer 1

The correct option is C $6$ and $36$

Solution in two variables
Let the present age of father's be $x$ years and present age of son's be $y$ years.
According to the problem
$x=6y$
After $4$ years
$x+4=4(y+4)$
Hence we get two equations
$x=6y$ ......... $\left(1\right)$
$x+4=4(y+4)$ ..... $\left(2\right)$
Simplifying eq $\left(2\right)$
$x+4=4y+16$
$x-4y=12$
Put $x=6y$ in eq $\left(2\right)$, we get
$6y-4y=12$
$2y=12$
$y=6$ years
and $x=6y=36$ years
Present age of son $=6$ years
and present age of father $=36$ years

Solution in one variable

Let, the present age of the son be $x$ years.

Therefore, father's present age $=6x$ years​

$4$ years form now,

Son's age $=x+4$ years

Father's age $=6x+4$ years

Now, according to the question,

$\Rightarrow 6x+4=4(x+4)$

$\Rightarrow 6x+4=4x+16$

$\Rightarrow 6x-4x=16-4$

$\Rightarrow 2x=12$

$\Rightarrow x=6$

Therefore,

Present age of Son $=x=6$ years

Present age of father $=6x=36$ years