Pipe C alone can empty a tank in 21 hours. Pipes A and B alone can fill the same tank in 7 hours and 14 hours, respectively. If pipes A and C are opened together until 50% of the tank is filled and the rest is filled by pipe B alone, find the total time taken to fill the tank.

ATQ, Let, the total work = 42 units (LCM of 21, 7 and 14) The efficiency of pipe A = 42/7 = 6 units/hour The efficiency of pipe B = 42/14 = 3 units/hour The efficiency of pipe C = 42/21 = 2 units/hour 50% of the tank = 42 × 50/100 = 21 units The time taken to fill 50% tank by pipes A and C together = 21 / (6 − 2) = 21 / 4 = 5.25 hours Remaining work = 21 units The time taken to fill the remaining tank by pipe B = 21 / 3 = 7 hours Total time taken = (5.25 + 7) = 12.25 hours