Pipes A and B can fill an empty tank in 6 and 8 hours respectively, while pipe C can empty the full tank in 10 hours. If all three pipes are opened together, then the tank will get filled in:

$5\frac{5}{23}$hrs

A+ = 6 hrs, B+ = 8 hrs, C- = 10 hrs,

⇒ Time required by A + B + C to completely fill the cistern = \(\frac{120}{20+15-12}\) = \(\frac{120}{23}\) = \( {5 }_{23 }^{5 } \) hrs.