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

Pipes A can fill a tank in 8 hours
Pipes A can fill 1/8 portion of a tank in 1 hour

Pipes B can fill a tank in 6 hours
Pipes B can4 fill 1/6 portion of a tank in 1 hour

Pipe C can empty it in 12 hours.
Pipe C can empty 1/12 portion of it in 1 hour.

Pipes A, B and C together can fill (1/8 + 1/6 - 1/12) = (3 + 4 - 2)/24
or 5/24portion of a tank in 1 hour


∴The tank will be full in 24/5 hours