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

Let us assume the quantity of tank to be 60 L i.e. the LCM of 12, 15 and 20.
Efficiencies of pipes A, B and C are 5, 4 and 3 L per hr resepectively.
Efficiency on hour 1 = A + B = 9 L per hr.
Efficiency on hour 2 = A + C = 8 L per hr.
In 2 hrs, 9+8 = 17 L of water is filled.
In 6 hrs i.e. 3 cycles, 17*3 = 51 L of water will be filled.
The remaining 9 L will be filled by A + B on the next hour thus filling the tank in 6+1 = 7 hours.