Pipe A and B can fill a tank in 20 hours and 25 hours respectively, and pipe C can empty the full tank in 40 hours. If all the pipes are opened together, then how much time will be needed to make the tank full?

$15\frac{5}{13}$ hours

The correct answer is Option (3) → $15\frac{5}{13}$ hours **

Rate of pipe A $=\frac{1}{20}$ tank/hour

Rate of pipe B $=\frac{1}{25}$ tank/hour

Rate of pipe C (emptying) $=-\frac{1}{40}$ tank/hour

Net rate:

$\frac{1}{20}+\frac{1}{25}-\frac{1}{40}$

LCM = 200

$\frac{10}{200}+\frac{8}{200}-\frac{5}{200}=\frac{13}{200}$

Time required $=\frac{1}{\frac{13}{200}}=\frac{200}{13}$ hours

Required time = $\frac{200}{13}$ hours