Management Aptitude Test Dec 2019 Paper

Let the speed of the motorboat in still water be $\mathit{x}\mathrm{km}∕\mathrm{h}$. Then,
Downstream speed $=\left(\mathit{x}+2\right)\mathrm{km}∕\mathrm{h}$
Upstream speed $=\left(\mathit{x}-2\right)\mathrm{km}∕\mathrm{h}$
$\therefore \frac{5}{\mathit{x}+2}+\frac{5}{\mathit{x}-2}=\frac{4}{3}$
$\Rightarrow \frac{1}{\mathit{x}+2}+\frac{1}{\mathit{x}-2}=\frac{4}{15}$
$\Rightarrow \frac{2\mathit{x}}{{\mathit{x}}^2-4}=\frac{4}{15}$
$\Rightarrow 4{\mathit{x}}^2-30\mathit{x}-16=0$
$\Rightarrow 2{\mathit{x}}^2-15\mathit{x}-8=0$
$\Rightarrow 2{\mathit{x}}^2-16\mathit{x}+\mathit{x}-8=0$
$\Rightarrow 2\mathit{x}\left(\mathit{x}-8\right)+1\left(\mathit{x}-8\right)=0$
$\Rightarrow \left(\mathit{x}-8\right)\left(2\mathit{x}+1\right)=0$
$\Rightarrow \mathit{x}=8$ [as $\mathit{x}$ cannot be negative]
Hence, speed of motorboat in still water = 8 km/h