CONCEPT: Pipes and Cisterns

Effective filling work done =Filing efficiency-Emptying efficiency

SOLUTION:

Let the capacity of the tank be LCM(10,12,20)= 120 units

Efficiency of pipe A =12 units (+filling)

Efficiency of pipe B =10 units (+filling)

Efficiency of pipe C = 6 units (-emptying)

Total parts of the tank filled in an hour 12+10-6=16 units

Hence the time taken to fill in the tank is 120/16=15/2 =7.5hrs (A)