Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. The number of hours taken by C alone to fill the tank is:

Explanation:-

$$\eqalign{ & {\text{Part}}\,{\text{filled}}\,{\text{in}}\,{\text{2}}\,{\text{hours}}\, = \frac{2}{6} = \frac{1}{3} \cr & {\text{Remaining}}\,{\text{part}} = \left( {1 - \frac{1}{3}} \right) = \frac{2}{3} \cr & \therefore \left( {A + B} \right)'{\text{s}}\,{\text{7}}\,{\text{hour's}}\,{\text{work}} = \frac{2}{3} \cr & \left( {A + B} \right)'{\text{s}}\,{\text{1}}\,{\text{hour's}}\,{\text{work}} = \frac{2}{{21}} \cr & \therefore C'\,{\text{s}}1\,{\text{hour's}}\,{\text{work}} \cr & = \left\{ {\left( {A + B + C} \right)'{\text{s}}\,{\text{1}}\,{\text{hour's}}\,{\text{work}}} \right\} - \cr & \,\,\,\,\,\,\left\{ {\left( {A + B} \right)'{\text{s}}\,{\text{1}}\,{\text{hour's}}\,{\text{work}}} \right\} \cr & = \left( {\frac{1}{6} - \frac{2}{{21}}} \right) = \frac{1}{{14}} \cr & \therefore C\,{\text{alone}}\,{\text{can}}\,{\text{fill}}\,{\text{the}}\,{\text{tank}}\,{\text{in}}\,{\text{14}}\,{\text{hours}} \cr}$$