arithmetic - 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 - skillgun

(A + B)'s 1 hour's work = 1/ + 1/15 = 9/6 = 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.
Total time taken to fill the tank = (6 + 1) hrs = 7 hrs