SSC CHSL Model Paper 18

Let the total number of students be x.
Number passed in one or both is given by:
$\mathit{n}\left(\mathit{A}\cup \mathit{B}\right)=\mathit{n}\left(\mathit{A}\right)+\mathit{n}\left(\mathit{B}\right)-\mathit{n}\left(\mathit{A}\cap \mathit{B}\right)$ = 65% of x + 60% of x - 40% of x
$=\frac{65\mathit{x}}{100}+\frac{60\mathit{x}}{100}-\frac{40\mathit{x}}{100}$
$=\frac{85\mathit{x}}{100}=\frac{17\mathit{x}}{20}$
Failed in both = $\mathit{x}-\frac{17\mathit{x}}{20}=\frac{3\mathit{x}}{20}$.
So $\frac{3\mathit{x}}{20}=90\Rightarrow \mathit{x}=\frac{90\times 20}{3}=600$
Thus, total number of students are 600