A tank when full can be emptied by an outlet pipe A in 5.6 hours, while an inlet pipe B can fill the same empty tank in 7 hours. If pipes A and B are turned on alternatively for 1 hour each starting with pipe A when the tank is full, how long will it take to empty the tank?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 47 hours.
Time required for Pipe A to empty the tank = 5.6 hours
Time required for Pipe A to fill the tank = 7 hours
Total work = LCM of 5.6 and 7 = 28
Efficiency of Pipe A = 28/5.6 = 5
Efficiency of Pipe A = 28/7 = 4
Pipes A and B are turned on alternatively for 1 hour each starting with pipe A.
Work done by both pipes in 2 hours = -5 + 4 = -1 unit
At the last hour, pipe A will work alone, hence 5 units will be done by pipe A.
The remaining work = 28 - 5 = 23 units are done by Pipe A and Pipe B.
Time required to complete remaining work = 23 × 2 = 46 hours
Total time required = 46 + 1 = 47 hours
Therefore, a total of 47 hours will required to empty the tank.