Two pipes A and B can fill a cistern in 12 and 25 hours, respectively. The pipes are opened simultaneously and it is found that due to a leakage in the bottom. It took 1 hour 40 minutes more to fill the cistern. When the cistern is full, in how much time will the leak empty the cistern?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 50 hours.
LCM of 12.5 and 25 = 25 units
Let the capacity of the cistern be 25 units
Efficiency of A = 25/12.5 = 2 units
Efficiency of B = 25/25 = 1 unit
Efficiency of (A + B) = 2 + 1 = 3 units
Time taken by A and B to fill the cistern without leakage = 25/3 = 8(1/3) hours = 8 hours 20 mins
Time taken by A and B to fill the cistern with leakage = 8 hours 20 mins + 1 hour 40 mins = 10 hours
The combined efficiency of A and B with leakage = 25/10 = 2.5 units/hr
⇒ Efficiency of leakage = 3 - 2.5 = 0.5 units/hr
Time required by the leak to empty the full cistern = 25/0.5 = 50 hours
Hence,
The leak can empty the full cistern in 50 hours