Sainik School Entrance Exam 2020 Solved Paper

(b) Suppose that 8 years ago, ages of $\mathit{x}$ and $\mathit{y}$ are $7\mathit{x}$ years and $6\mathit{x}$ years
Then, present age of $\mathit{x}=7\mathit{x}+8$ years
and, present age of $\mathit{y}=6\mathit{x}+8$ years
∴ Sum of their ages 8 years from now
$=7\mathit{x}+8+8+6\mathit{x}+8+8$ years
$=13\mathit{x}+32$ years
By options
(a) $13\mathit{x}+32=82$
$\Rightarrow 13\mathit{x}=50\therefore \mathit{x}=\frac{50}{13}$
$50$ is not divisible by $13$
(b) $13\mathit{x}+32=97$
$\Rightarrow 13\mathit{x}=97-32$
$\Rightarrow 13\mathit{x}=65$
$\Rightarrow \mathit{x}=5$
(c) $13\mathit{x}+32=75$
$\Rightarrow 13\mathit{x}=43\therefore \mathit{x}=\frac{43}{13}$
$43$ is not divisible by $13$
(d) $13\mathit{x}+32=94$
$\Rightarrow 13\mathit{x}=62\therefore \mathit{x}=\frac{62}{13}$
$62$ is not divisible by $13.$