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:

Let's assume the total capacity of the tank is 24 units.

Pipes A and B can empty a full tank in 8 and 12 hours respectively.

The efficiency of pipe A = $$\frac{24}{8}$$ = -3 units/hour (Here negative sign represents that the pipe is used to empty the tank.)

The efficiency of pipe B = $$\frac{24}{12}$$ = -2 units/hour (Here negative sign represents that the pipe is used to empty the tank.)

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.

When all pipes were opened then one-sixth of the tank got emptied in one hour. It means that the entire tank got empty = $$6\times1$$ = 6 hours.

The efficiency of pipes A, B and C together = $$\frac{24}{6}$$ = -4 units/hour

efficiency of A + efficiency of  B + efficiency of C = -4

(-3) + (-2) + efficiency of C = -4

-3 -2 + efficiency of C = -4

-5 + efficiency of C = -4

efficiency of C = 5-4 = 1 unit/hour

Time taken by C alone to fill the tank = $$\frac{24}{1}$$

= 24 hours