NIFT PG 2014 Question Paper with solutions

Tank filled by A, B and C together in one hour
$\frac{1}{\mathit{A}}+\frac{1}{\mathit{B}}+\frac{1}{\mathit{C}}=\frac{1}{6}$...(i)
Portion of tank remaining empty after 2 hrs filling
$=1-2\times \frac{1}{6}=\frac{2}{3}$tank
A and B can fill remaining tank in 7 hrs.
$\therefore \frac{1}{\mathit{A}}+\frac{1}{\mathit{B}}=\frac{\frac{2}{3}}{7}$
$\Rightarrow \frac{1}{\mathit{A}}+\frac{1}{\mathit{B}}=\frac{2}{21}$...(ii)
From (i) and (ii), we get
$\frac{1}{\mathit{C}}=\frac{1}{6}-\frac{2}{12}=\frac{3}{42}=\frac{1}{14}$
∴ C alone can fill the tank in 14 hours.