SSC GD Constable 4 Feb 2025 Shift 1 Paper

A number is first decreased by $15\%$ and then increased by $20\%$. The number so obtained is 78 more than the original number.
Calculation:
Let the original number be x .
After decreasing by $15\%$, the number becomes $\mathit{x}-0.15\mathit{x}=0.85\mathit{x}$
After increasing by $20\%$, the number becomes $0.85\mathit{x}+0.20\left(0.85\mathit{x}\right)=0.85\mathit{x}+0.17\mathit{x}=1.02\mathit{x}$
According to the given condition:
$1.02\mathit{x}=\mathit{x}+78$
$\Rightarrow 0.02\mathit{x}=78$
$\Rightarrow \mathit{x}=78∕0.02$
$\Rightarrow \mathit{x}=3900$