SSC CGL 18 Aug 2021 Shift 2 Paper

Given, Average of $\mathit{x}$ occurring 5 times and y occurring 7 times is 37 .
$\Rightarrow 5\mathit{x}+7\mathit{y}=37\times \left(5+7\right)$
$\Rightarrow 5\mathit{x}+7\mathit{y}=37\times 12$ . . . (i)
Average of $\mathit{x}$ occurring 7 times and $\mathit{y}$ occurring 5 times is 35
$\Rightarrow 7\mathit{x}+5\mathit{y}=35\left(7+5\right)$ . . . (ii)
From Eq. (i) and Eq. (ii),
$\left(5\mathit{x}+7\mathit{y}=37\times 12\right)\times 7$
and $\left(7\mathit{x}+5\mathit{y}=35\times 12\right)\times 5$
We get, $35\mathit{x}+49\mathit{y}=37\times 12\times 7$
$-35\mathit{x}\pm 25\mathit{y}=-35\times 12\times 5$
$\Rightarrow 24\mathit{y}=12\left(37\times 7-35\times 5\right)$
$\Rightarrow 24\mathit{y}=12\times 84$
$\therefore \mathit{y}=42$