Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If a is open all the time and B and C are open for one hour each alternately, the tank will be full in:

(A + B)'s 1 hour's work = (1/12 + 1/15)

= 9/60 = 3/20.

(A + C)'s hour's work =(1/12 + 1/20)

= 8/60 = 2/15.

Part filled in 2 hrs = (3/20 + 2/15) = 17/60.

Part filled in 6 hrs = (3 x 17/60) = 17/20.

Remaining part =(1 – 17/20) = 3/20.

Now, it is the turn of A and B and 3/20 part is filled by A and B in 1 hour.

Therefore, Total time taken to fill the tank = (6 + 1) hrs = 7 hrs.