SSC GD Constable 4 Feb 2025 Shift 3 Paper

Speed of boat in still water
Downstream speed = Speed of boat in still water + Speed of the stream
Upstream speed $=$ Speed of boat in still water - Speed of the stream
Calculation:
Let the speed of the boat in still water be $\mathit{x}\mathit{k}\mathit{m}∕\mathit{h}$.
Downstream speed $=\mathit{x}+9\mathit{k}\mathit{m}∕\mathit{h}$
Upstream speed $=\mathit{x}-9\mathit{k}\mathit{m}∕\mathit{h}$
Time taken to travel downstream $=56∕\left(\mathit{x}+9\right)$
Time taken to travel upstream $=28$ / ( $\mathit{x}-9$ )
Total time $=7$ hours
$\Rightarrow 56∕\left(\mathit{x}+9\right)+28∕\left(\mathit{x}-9\right)=7$
Multiply both sides by $\left(\mathit{x}+9\right)\left(\mathit{x}-9\right)$ :
$\Rightarrow 56\left(\mathit{x}-9\right)+28\left(\mathit{x}+9\right)=7\left(\mathit{x}+9\right)\left(\mathit{x}-9\right)$
$\Rightarrow 56\mathit{x}-504+28\mathit{x}+252=7\left({\mathit{x}}^2-81\right)$
$\Rightarrow 84\mathit{x}-252=7{\mathit{x}}^2-567$
Rearrange the equation:
$\Rightarrow 7{\mathit{x}}^2-84\mathit{x}-315=0$
Divide the entire equation by 7 :
$\Rightarrow {\mathit{x}}^2-12\mathit{x}-45=0$

Factorize the quadratic equation:
$\Rightarrow \left(\mathit{x}-15\right)\left(\mathit{x}+3\right)=0$

Since speed cannot be negative, $\mathit{x}=15\mathit{k}\mathit{m}∕\mathit{h}$.