B. 1 7/11
Feedback Let the time taken to fill the cistern by 3 taps A, B and C be X, Y, and Z minutes respectively.
Then the short cut formula for,
Time taken to fill the tank when all the pipes are opened = XYZ/(XY + YZ + ZX) minutes
Here, X = 9 minutes, Y = 6 minutes and Z = 3 minutes.
Now the required time = (9)(6)(3)/(9x6)+(6x3)+(3x9) minutes
= 9x6x3 / 54 + 18 + 27
= 9x6x3 / 9{6+2+3} = 6x3/6+2+3 = 18/11 = 1 + 7/11 minutes
Hence the answer is 1 7/11 minutes.