Pipes A and B can fill a tank in 6 hours and 8 hours respectively and pipe C can empty the full tank...........

Quantitative Aptitude (CPO) Time and work

Pipes A and B can fill a tank in 6 hours and 8 hours respectively and pipe C can empty the full tank in 12 hours. All three pipes are

opened together. but pipe A is closed after 3 hours. In how many hours will the remaining part of the tank be filled?

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SSC CPO 12th-March-2019-Shift-2

- Pipe A fills the tank in 6 hours, so it fills 1/6 of the tank in an hour.

- Pipe B fills the tank in 8 hours, so it fills 1/8 of the tank in an hour.

- Pipe C empties the tank in 12 hours, so it empties 1/12 of the tank in an hour.

- When all three pipes are opened together, their combined rate is: (1/6 + 1/8 - 1/12) of the tank per hour.

- Simplifying: (4/24 + 3/24 - 2/24) = 5/24 of the tank per hour.

- In the first 3 hours, 3 x 5/24 = 15/24 = 5/8 of the tank is filled.

- Remaining part = 1 - 5/8 = 3/8 of the tank.

- After closing pipe A, only pipes B and C work with a rate of (1/8 - 1/12) = 1/24 of the tank per hour.

- For 3/8 of the tank to be filled at this rate, it takes (3/8) / (1/24) = 9 hours.

Option:2 - 9 is correct.

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