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# Pipe A can fill a Tank in 18 Hours, Pipe B can empty a Tank in 12 Hour

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Intern
Joined: 26 Mar 2019
Posts: 12
Pipe A can fill a Tank in 18 Hours, Pipe B can empty a Tank in 12 Hour  [#permalink]

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Updated on: 26 Mar 2019, 05:29
2
00:00

Difficulty:

55% (hard)

Question Stats:

58% (02:15) correct 42% (03:10) wrong based on 31 sessions

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Pipe A can fill a Tank in 18 Hours, Pipe B can empty a Tank in 12 Hours, Pipe C can fill Tank in 6 Hours. The Tank is already filled up to 1/6 of its capacity. Now Pipe A is opened in the First Hour alone, Pipe B is opened in the Second Hour alone and Pipe C is opened in the Third Hour alone. This cycle is repeated until the Tank gets filled. Then in How many Hours does the rest of Tank gets filled?

A. 15 Hours
B. 18 Hours
C. 20 Hours
D. 24 Hours
E. None

Originally posted by Wasif007 on 26 Mar 2019, 05:26.
Last edited by Bunuel on 26 Mar 2019, 05:29, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
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Re: Pipe A can fill a Tank in 18 Hours, Pipe B can empty a Tank in 12 Hour  [#permalink]

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26 Mar 2019, 07:25
1
let the total work be 36 units (a common multiple for 18,12 & 6)
so per 1 hour, A would pump in 2 units, B would pump out 3 units & C would pump in 6 units
so 1 cycle of 3 hours would add 5 units in.

As $$\frac{1}{6}$$ is already filled, so 6 units are already there.

at zero time: 6 units
after 3 hour (1 cycle): 6 + (2-3+6) = 6 + 5(1) = 11 , ... and so on .....

to fill the 36 units:
36 = 6 + 5x , where x is the number of cycles
x = 6, which represent 3 hours each, so 18 hours

so B
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Re: Pipe A can fill a Tank in 18 Hours, Pipe B can empty a Tank in 12 Hour  [#permalink]

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27 Mar 2019, 19:08
Wasif007 wrote:
Pipe A can fill a Tank in 18 Hours, Pipe B can empty a Tank in 12 Hours, Pipe C can fill Tank in 6 Hours. The Tank is already filled up to 1/6 of its capacity. Now Pipe A is opened in the First Hour alone, Pipe B is opened in the Second Hour alone and Pipe C is opened in the Third Hour alone. This cycle is repeated until the Tank gets filled. Then in How many Hours does the rest of Tank gets filled?

A. 15 Hours
B. 18 Hours
C. 20 Hours
D. 24 Hours
E. None

We can see that for 3 consecutive hours, the tank is filled 1/18 - 1/12 + 1/6 = 2/36 - 3/36 + 6/36 = 5/36 of its capacity. Since 5/6 of the tank still needs to be filled and (5/6)/(5/36) = 6, we need 3 x 6 = 18 hours to fill the rest of the tank.

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Re: Pipe A can fill a Tank in 18 Hours, Pipe B can empty a Tank in 12 Hour   [#permalink] 27 Mar 2019, 19:08
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