Management Aptitude Test 2017 Paper

(c) 108 days
Let, A, B and C complete the work in x, y and z days, respectively.
According to the question,
$\frac{1}{\mathit{x}}+\frac{1}{\mathit{y}}+\frac{1}{\mathit{z}}=\frac{1}{36}$ ......(i)
and $\frac{1}{\mathit{x}}+\frac{1}{\mathit{y}}=\frac{2}{\mathit{z}}$ ........(ii)
and $\frac{1}{\mathit{x}}+\frac{1}{\mathit{z}}=\frac{3}{\mathit{y}}$ ........(iii)
On solving Eqs. (i) and (ii), we get
$\frac{1}{\mathit{x}}+\frac{1}{\mathit{y}}+\frac{1}{\mathit{z}}=\frac{1}{36}$
⇒ $\frac{2}{\mathit{z}}+\frac{1}{\mathit{z}}=\frac{1}{36}$ ⇒ $\frac{3}{\mathit{z}}=\frac{1}{36}$
⇒ z = 108 days
∴ C completes the work in 108 days.