SSC CGL 24 Aug 2021 Shift 3 Paper

Given, Distance $=150\mathit{k}\mathit{m}$
Speed of motor boat $\left(\mathit{x}\right)=20\mathit{k}\mathit{m}∕\mathit{h}$
Total time $=16\mathit{h}$
Let Speed of flow of river $\left(\mathit{y}\right)=$ ?
When boat move downstream $=20+\mathit{y}$
When boat move upstream $=20-\mathit{y}$
Speed
Time
$\Rightarrow 16=\frac{150}{\left(20+\mathit{y}\right)}+\frac{150}{\left(20-\mathit{y}\right)}$
$\Rightarrow 16=\frac{150\left(20-\mathit{y}\right)+150\left(20+\mathit{y}\right)}{{\left(20\right)}^2-{\mathit{y}}^2}$
$\Rightarrow 16\times {20}^2-16{\mathit{y}}^2$
$=150\times 20-150\mathit{y}+150\times 20+150\mathit{y}$
$\Rightarrow 16\times 400-16{\mathit{y}}^2=3000+3000$
$\left[\because \left(\mathit{a}-\mathit{b}\right)\left(\mathit{a}+\mathit{b}\right)={\mathit{a}}^2-{\mathit{b}}^2\right]$
$\Rightarrow 16{\mathit{y}}^2=6400-6000$
$\Rightarrow 16{\mathit{y}}^2=400$
$\Rightarrow {\mathit{y}}^2=25$
$\Rightarrow \mathit{y}=5\mathit{k}\mathit{m}∕\mathit{h}$
Speed of flow of the river $=5\mathit{k}\mathit{m}∕\mathit{h}$.