Each inlet pipe can fill an empty cistern in 84 hours while each drain pipe can empty the same cistern from a filled condition in 105 hours. When the cistern is empty, 9 inlet pipes and 10 outlet pipes are simultaneously opened. After how many hours will the cistern be completely filled?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 84.
Total work = Efficieicny × Time
Now,
Total work (LCM of 84 and 105) = 420 units
Efficiency of 1 inlet pipe = 420/84 = 5
Efficiency of 1 outlet pipe = 420/105 = 4
Total efficiency of 9 inlet pipe = 9 × 5 = 45
Total efficiency of 10 outlet pipe = 10 × 4 = 40
Total efficiency = 45 - 40 = 5
Hence, the required time taken = 420/5 = 84 hours