Pipes A and B can fill a tank in 40 hours and 50 hours respectively and pipe C can empty the full tank in 60 hours. If all the pipes are opened together, how much time (in hours ) will be needed to fill the tank ?

$35\frac{5}{17}$

The correct answer is Option (2) → $35\frac{5}{17}$

Rate of A = $\frac{1}{40}$ tank/hr

Rate of B = $\frac{1}{50}$ tank/hr

Rate of C = $-\frac{1}{60}$ tank/hr

∴ Combined Rate = $\left(\frac{1}{40}+\frac{1}{50}-\frac{1}{60}\right)=\frac{17}{600}$ tank/hr

$⇒Time=\frac{1}{Combined\,Rate}=\frac{600}{17}hr=35\frac{5}{17}$ hour