Pipes A and B can empty a full tank in 8 and 12 hours, respectively. C is a filling pipe. All the three pipes were opened together at the same time and one-sixth of the tank got emptied in one hour. C alone can fill the tank in:

24 hours

A- = 8 hrs, B- = 12 hrs, A + B + C = 1\(\frac{1}{6}\) = 1hr = 6 hrs,

⇒ A + B + C = -4    (Efficiency)

⇒ -3 -2 + C = -4

⇒ -5 + C = -4

⇒ C = 1,

Time required by C to fill the tank alone = \(\frac{24}{1}\) = 24 hrs.