RRB Group D 8-Dec-2013 Shift 1 Solved Paper

Let the present age of the man be x
The present age of son = y
One year ago, his age = x – 1
One year ago, age of son = y – 1
According to the question:
$\left(\mathit{x}-1\right)=7\left(\mathit{y}-1\right)$
$\Rightarrow \mathit{x}-1=7\mathit{y}-7$
$\Rightarrow \mathit{x}-7\mathit{y}=-6\left(1\right)$
Also, $\mathit{x}={\mathit{y}}^2\left(2\right)$
By (1) and (2)
${\mathit{y}}^2-7\mathit{y}=-6$
$\Rightarrow {\mathit{y}}^2-7\mathit{y}+6=0$
$\Rightarrow {\mathit{y}}^2-6\mathit{y}-\mathit{y}+6=0$
$\Rightarrow \left(\mathit{y}-6\right)\left(\mathit{y}-1\right)=0$
$\therefore \mathit{y}=6$
Son's present age $=6$ years.
Father's present age $=36$ years