Management Aptitude Test 2016 Paper

(c) Let P and Q together take x h to complete the work.
Then, time taken by P alone = (x + 8) hand
time taken by Q alone = (x + $\frac{9}{2}$ ) h
According to the question,
$\frac{1}{\left(\mathit{x}+8\right)}+\frac{1}{\left(\mathit{x}+\frac{9}{2}\right)}=\frac{1}{\mathit{x}}$
⇒ $\frac{1}{\left(\mathit{x}+8\right)}+\frac{2}{\left(2\mathit{x}+9\right)}=\frac{1}{\mathit{x}}$
⇒ $\frac{2\mathit{x}+9+2\mathit{x}+16}{\left(\mathit{x}+8\right)\left(2\mathit{x}+9\right)}=\frac{1}{\mathit{x}}$
⇒ $\mathit{x}\left(4\mathit{x}+25\right)=2{\mathit{x}}^2+72+16\mathit{x}+9\mathit{x}$
⇒ $4{\mathit{x}}^2+25\mathit{x}=2{\mathit{x}}^2+72+25\mathit{x}$
⇒ $\mathrm{2}{\mathit{x}}^2=72$
⇒ ${\mathit{x}}^2=36$
⇒ $\mathit{x}=6$h