Management Aptitude Test 2016 Paper

(b) Let time taken by A and B together to complete thework be x days.
Then, time taken by A alone to complete the work = (x+27)days
Time taken by B alone to complete the work= (x + 3) days
According to the question,
$\frac{1}{\left(\mathit{x}+27\right)}+\frac{1}{\left(\mathit{x}+3\right)}=\frac{1}{\mathit{x}}$
$\Rightarrow \frac{\left(\mathit{x}+3\right)+\left(\mathit{x}+27\right)}{\left(\mathit{x}+27\right)\left(\mathit{x}+3\right)}=\frac{1}{\mathit{x}}$
$\Rightarrow \mathit{x}\left(2\mathit{x}+30\right)={\mathit{x}}^2+30\mathit{x}+81$
$\Rightarrow 2{\mathit{x}}^2+30\mathit{x}={\mathit{x}}^2+30\mathit{x}+81$
${\mathit{x}}^2=81$
$\mathit{x}=9$