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Pipe A can fill a tank in 3 hours. Pipe B can empty the same

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gmatquant25
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Pipe A can fill a tank in 3 hours. Pipe B can empty the same [#permalink] New post   Updated on: 27 May 2013, 03:30
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Pipe A can fill a tank in 3 hours. Pipe B can empty the same tank in 2 hours. If the tank is initially two thirds full then in how many hours will the tank be completely empty in if both the pipes are turned on simultaneously?

(A) 2 hours
(B) 3 hours
(C) 4 hours
(D) 5 hours
(E) 9 hours
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C

Originally posted by gmatquant25 on 27 May 2013, 03:16.
Last edited by gmatquant25 on 27 May 2013, 03:30, edited 1 time in total.
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Re: Pipe A can fill a tank in 3 hours. Pipe B can empty the same [#permalink] New post   27 May 2013, 03:32
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gmatquant25 wrote:
Pipe A can fill a tank in 3 hours. Pipe B can empty the same tank in 2 hours. If the tank is initially two thirds full then in how many hours will the tank be completely empty in if both the pipes are turned on simultaneously?

(A) 2 hours
(B) 3 hours
(C) 4 hours
(D) 5 hours


The 2/3 of the tank will be emptied in \((time)=\frac{(job)}{(rate)}=\frac{\frac{2}{3}}{\frac{1}{2}-\frac{1}{3}}=4\) hours (1/2-1/3 is the rate at which the tank is emptied).

Answer: C.

Hope it's clear.
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Re: Pipe A can fill a tank in 3 hours. Pipe B can empty the same [#permalink] New post   27 May 2013, 03:55
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Rate of filling the tank by A =1/3
Rate of emptying the tank by B =1/2
Combined rate of emptying the tank = 1/2-1/3 =1/6
2/3rd of tank needs to be emptied.
R=w/t
1/6=(2/3)*(1/t)
On simplifying , t= 4 hrs

Hope that helps!!!

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Re: Pipe A can fill a tank in 3 hours. Pipe B can empty the same [#permalink] New post   27 May 2013, 03:21
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gmatquant25 wrote:
Pipe A can fill a tank in 3 hours. Pipe B can empty the same tank in 2 hours. If the tank is initially two thirds full then in how many hours will the tank be completely empty in if both the pipes are turned on simultaneously?
(A)2 hours
(B)3 hours
(C)4 hours
(D)5 hours


Lets say tank contains 6 liters
Pipe A works at \(\frac{6}{3}= 2\) liters every hour (added)=\(+2\)
Pibe B works ar \(\frac{6}{2}= 3\) liters every hour (subtracted)=\(-3\)

The tank is 2/3 full so contains 4 liters, and the pipes combined give us a \(-3+2=-1\) liter every hour.(minus one liter every hour)
So they would take \(4\) hours to empty it.
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Re: Pipe A can fill a tank in 3 hours. Pipe B can empty the same [#permalink] New post   20 May 2017, 13:14
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Consider the tank to be 180 units.
Hence rate at which Pipe A fills the tank is 60 units(since it fills the tank in 3 hours)
Also, rate at which Pipe B empties the tank is 90 units(since it empties the tank in 2 hours)
It is given that the tank is 2/3rd's full or has 120 units of water in it.

We need to find the time to empty it completely given both the pipes are on.
Both the pipes being on, will reduce 30 units(+60 - 90) an hour
120 - 30(x) = 0
or x=4(Option C)
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Re: Pipe A can fill a tank in 3 hours. Pipe B can empty the same [#permalink] New post   29 Oct 2019, 11:38
gmatquant25 wrote:
Pipe A can fill a tank in 3 hours. Pipe B can empty the same tank in 2 hours. If the tank is initially two thirds full then in how many hours will the tank be completely empty in if both the pipes are turned on simultaneously?

(A) 2 hours
(B) 3 hours
(C) 4 hours
(D) 5 hours
(E) 9 hours

Let the capacity of the tank be 6 units

So, Efficiency of Pipe A is + 2 units/hr
And , Efficiency of Pipe B is -3 units/hr

Combined Efficiency of both the pipes is -1 unit/ Hour

Quote:
If the tank is initially two thirds full then in how many hours will the tank be completely empty in if both the pipes are turned on simultaneously?


Capacity of water in the tank is 2/3*6 = 4 units

So, Time required to empty it will be 4/1 = 4 Hours, Answer must be (C)
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Re: Pipe A can fill a tank in 3 hours. Pipe B can empty the same [#permalink] New post   19 Jan 2022, 06:55
My solution:

x = full capacity of tank

A fills tank (x/3h) and B empties tank at (x/2h)

Net Outflow: (x/3h) - (x/2h) = - (1/6)*x / h

This means, that 1/6 of the full tank is emptied per hour, so the full tank would be empty in 6 hours. Since the tank now is only 2/3 full, it would only take 6 * (2/3) hours = 4 h to empty the tank.

Correct answer: C
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Re: Pipe A can fill a tank in 3 hours. Pipe B can empty the same [#permalink]
19 Jan 2022, 06:55
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