Management Aptitude Test Sep 2020 Paper

${\left(\mathit{A}+\mathit{B}\right)}^{\prime }\mathit{s}$ one day work $=\frac{1}{5}$
$\Rightarrow \left(\mathit{A}+\mathit{B}\right)=\frac{1}{5}$
By given condition,
$2\mathit{A}+\frac{1}{2}\mathit{B}=\frac{1}{4}$
On multiplying Eq. (i) by $\frac{1}{2}$,
we get
$\frac{1}{2}\cdot \mathit{A}+\frac{1}{2}\cdot \mathit{B}=\frac{1}{10}$
On Eq. (iii) subtracted from Eq.(ii), we get
$2\mathit{A}+\frac{1}{2}\mathit{B}=\frac{1}{4}$
$\frac{1}{2}\cdot \mathit{A}+\frac{1}{2}\cdot \mathit{B}=\frac{1}{10}$
$---$
$\left(2-\frac{1}{2}\right)\mathit{A}=\frac{1}{4}-\frac{1}{10}$
$\Rightarrow \frac{3}{2}\mathit{A}=\frac{5-2}{20}\Rightarrow \frac{3}{2}\mathit{A}=\frac{3}{20}\Rightarrow \frac{\mathit{A}}{2}=\frac{1}{20}$
$\therefore \mathit{A}=\frac{1}{10}$
Hence, $\mathit{A}$ alone would dothat work in 10 days.