Pipes A and B can fill a tank in 6 hours and 8 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together the time in which the tank can be filled is :

$4\frac{4}{5}$ Hours

The correct answer is Option (4) → $4\frac{4}{5}$ Hours

Pipe A = $\frac{1}{6}$ of the tank per hour

Pipe B = $\frac{1}{8}$ of the tank per hour

Pipe C = $\frac{1}{12}$ of the tank per hour (emptying)

Combined Rate = $\frac{1}{6}+\frac{1}{8}-\frac{1}{12}=\frac{5}{24}$

Time taken = $\frac{24}{5}$ hours = $4\frac{4}{5}$ Hours