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Two inlet pipes P and Q can fill an empty tank in 5 hours and 4 hours respectively. There is an outlet pipe R in the tank which can empty the fully filled tank in 6 hours. Both the inlet pipes P and Q are opened to fill the empty tank, but after 3 hours it is observed that the outlet pipe is also open, immediately it is closed then find in how much time the tank will be completely filled after closing the outlet pipe R?

Two inlet pipes P and Q can fill an empty tank in 5 hours and 4 hours respectively. There is an outlet pipe R in the tank which can empty the fully filled tank in 6 hours. Both the inlet pipes P and Q are opened to fill the empty tank, but after 3 hours it is observed that the outlet pipe is also open, immediately it is closed then find in how much time the tank will be completely filled after closing the outlet pipe R? Correct Answer 20 minutes

Given:

P can fill an empty tank in 5 hours

Q can fill the same empty tank in 4 hours

R can empty the full tank in 6 hours

P and Q opened to fill the tank and  R was closed after 3 hours 

Formula Used:  

Work = Efficiency × Time

Calculation:

Total work = LCM of 4, 5, 6

⇒ Total work = 60

Efficiency of inlet pipe P = 60/5

⇒ 12

Efficiency of inlet pipe Q = 60/4

⇒ 15

Efficiency of outlet pipe R = 60/6

⇒ 10

Tank is empty and after 3 hours outlet pipe is closed

Work done in 3 hours = 3(12 + 15 – 10)

⇒ 3 × 17

⇒ 51

Now, outlet pipe R is closed

Time taken by inlet pipes P and Q to fill the remaining tank = (60 – 51)/(12 + 15)

⇒ 9/27 hours = 1/3 hours = 20 minutes

∴ The tank will be completely filled after closing outlet pipe R in 20 minutes.

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