Pipes A and B can fill a tank in 18 hours and 27 hours, respectively, whereas pipe C can empty the full tank in 54 hours. All three pipes are opened together, but pipe C is closed after 12 hours. In how much time (in minutes) will one-third of the remaining part of the tank be filled by A and B together?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 24.
LCM(18, 27, and 54) = 54
The efficiency of Pipe A = 54/18 = 3 units
The efficiency of Pipe B = 54/27 = 2 units
The efficiency of Pipe C = 54/54 = -1 unit
Work done by all three pipes in 12 hours = (3 + 2 - 1) × 12 = 48 units
Remaining = 54 - 48 = 6 units
One-third of the tank = 1/3 × 6 = 2 units
Time taken by A and B = 2/(3 + 2) = 2/5 hours
2/5 × 60 = 24 minutes