(c) 14
Part of the tank filled by (A + B + C) in 2 hours = 2 x \(\frac{1}{6}\) = \(\frac{1}{3}\)
Remaining part = 1 - \(\frac{1}{3}\) = \(\frac{2}{3}\)
\(\therefore\) \(\frac{2}{3}\)rd of the tank is filled by (A + B) in 7 hours.
\(\therefore\) The whole tank is filled by (A + B) in \(\big(7\times\frac{3}{2}\big)\) hours = \(\frac{21}{2}\) hours
\(\therefore\) Part of the tank filled by C in 1 hour = Part of the tank filled by (A + B + C) in 1 hour - Part of the tank filled by (A + B) in 1 hour
= \(\frac{1}{6}\) - \(\frac{2}{21}\) = \(\frac{3}{42}\) = \(\frac{1}{14}\)
\(\therefore\) C can fill the whole tank in 14 hours.
