Inlet Pipes A and B can together fill an empty tank in 1.5 hours. Outlet Pipe C, when opened alone, can empty the completely filled tank, in 4.5 hours. When only Pipes A and C are opened together, the empty tank is filled in 6 hours. Find the time taken by Pipe B, when opened alone, to fill the empty tank.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 3 hours 36 minutes.
Given:
Inlet pipes A and B opened to fill the empty tank in = 1.5 hours = h
Outlet pipe C can empty the filled tank in = 4.5 hours = h
Only A and C together fill the tank in = 6 hours
Concept Used:
Total work = Efficiency × Time
Explanation:
Let the total capacity of tank be LCM ((), (), 6) = 18 units
The combined efficiency of inlet pipes A and B to fill the empty tank = 18 ÷ () = 12
The efficiency of outlet pipe C to empty the filled tank = 18 ÷ () = 4
The combined efficiency of A and C to fill the tank = 18 ÷ 6 = 3
According to the question
⇒ A + C = 3
⇒ A - 4 = 3
⇒ A = 7
So, A + B = 12
⇒ 7 + B = 12
⇒ B = 12 - 7 = 5
Hence, the empty tank is filled by B alone in = = 3 hours 36 minutes