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Tap A can fill a tank in 36 minutes, Tap B can fill the same

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Tap A can fill a tank in 36 minutes, Tap B can fill the same [#permalink]

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Tap A can fill a tank in 36 minutes, Tap B can fill the same tank in 48 minutes. If they are opened simultaneously, at what time tap B (keep tap A running) can be stopped so that the tank can be filled completely filled in 27 minutes.

A. 8
B. 12
C. 20
D. 30
E. 36

[Reveal] Spoiler:
This question was asked by one of the tutor who was giving presentation on a local GMAT prep course.I cannot remember the options exactly, but all options were integers. I guess b/w (12-40).If the question sounds awkward or has other flaws please feel free to provide inputs/correct it.I am looking for its solution and similar rate problems in which 2 entities work together for some portion and then one of 'em leaves.
[Reveal] Spoiler: OA

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Originally posted by conty911 on 27 Sep 2012, 10:21.
Last edited by bb on 05 Dec 2016, 10:25, edited 1 time in total.
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Re: Tap A can fill a tank in 36 minutes, Tap B can fill the same [#permalink]

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Tap A can fill a tank in 36 minutes which means that 1/36th of the tank will be filled up in a minute
Tap B can fill a tank in 48minutes which means that 1/48th of the tank will be filled up in a minute

and Given that A is open for 27 min --> 27/36 or 3/4 of the tank will be filled and B has to fill the remaing 1/4th of the tank.

B will fill the enitre tank in 48 mins and for it to fill 1/4 th of the tank it will take (48/4)12 mins.
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Re: Tap A can fill a tank in 36 minutes, Tap B can fill the same [#permalink]

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New post 27 Sep 2012, 10:35
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abhishekkpv wrote:
Tap A can fill a tank in 36 minutes which means that 1/36th of the tank will be filled up in a minute
Tap B can fill a tank in 48minutes which means that 1/48th of the tank will be filled up in a minute

and Given that A is open for 27 min --> 27/36 or 3/4 of the tank will be filled and B has to fill the remaing 1/4th of the tank.

B will fill the enitre tank in 48 mins and for it to fill 1/4 th of the tank it will take (48/4)12 mins.



Thanks that helps kudos to you .:)
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Re: Tap A can fill a tank in 36 minutes, Tap B can fill the same [#permalink]

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conty911 wrote:
Tap A can fill a tank in 36 minutes, Tap B can fill the same tank in 48 minutes. If they are opened simultaneously, at what time tap B (keep tap A running) can be stopped so that the tank can be filled completely filled in 27 minutes.

[Reveal] Spoiler:
This question was asked by one of the tutor who was giving presentation on a local GMAT prep course.I cannot remember the options exactly, but all options were integers. I guess b/w (12-40).If the question sounds awkward or has other flaws please feel free to provide inputs/correct it.I am looking for its solution and similar rate problems in which 2 entities work together for some portion and then one of 'em leaves.



You can also use two equations provided:
(1/36 + 1/48)t1 + (1/36)t2 =1
t1 + t2 = 27 -> t2 = 27 - t1

(1/36 + 1/48)t1 + (1/36)(27 - t1) = 1

t1 = 12
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Re: Tap A can fill a tank in 36 minutes, Tap B can fill the same [#permalink]

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A to be opened for 27 mins that is 27/36 =3/4 of the tank is filled..

so remaining 1/4th of tank to be filled by B

48 /4 = 12 mins to fill 1/4 of the remaining...(logic is 1/4 =x/48) !!
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Re: Tap A can fill a tank in 36 minutes, Tap B can fill the same [#permalink]

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New post 25 Oct 2012, 18:59
abhishekkpv wrote:
Tap A can fill a tank in 36 minutes which means that 1/36th of the tank will be filled up in a minute
Tap B can fill a tank in 48minutes which means that 1/48th of the tank will be filled up in a minute

and Given that A is open for 27 min --> 27/36 or 3/4 of the tank will be filled and B has to fill the remaing 1/4th of the tank.

B will fill the enitre tank in 48 mins and for it to fill 1/4 th of the tank it will take (48/4)12 mins.


Very good way of thinking. +1

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Re: Tap A can fill a tank in 36 minutes, Tap B can fill the same [#permalink]

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conty911 wrote:
Tap A can fill a tank in 36 minutes, Tap B can fill the same tank in 48 minutes. If they are opened simultaneously, at what time tap B (keep tap A running) can be stopped so that the tank can be filled completely filled in 27 minutes.


I would approach this question in some other way, since it says that the taps are opened simultaneously, and the question asks what time tap B can be stopped at interval "after both taps have been opened for some time" so that the entire tank can be filled in 27 minutes (not running tap A for addition 27 minutes).

1. find the combined rate of two taps (since they are opened simultaneously): work/time>>> (1/36+1/48) = 6/144, meaning that combined rate is 144/6 = 24 minutes (both taps can fill up the tank in 24 minutes if with no pause on either tap).

2. let T be the time that tap B can be stopped. we can form the work formula letting a+b run together for T + tap A alone continues running for 27-T (since total time is 27 minutes) = 1 (filling up the tank)

the equation looks like this : (1/24)T + (1/36)(27-T) = 1
>>> 3T/72 +(54-2T)/72 = 1
solve this equation you will get T = 18 minutes, the time that tap B can be stopped so that tank can be filled in 27 minutes, which is the answer.

in this case, tap A alone will continue running for 9 minutes to fill up the tank.
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Re: Tap A can fill a tank in 36 minutes, Tap B can fill the same [#permalink]

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Rate of B x time + Rate of A x 27 minutes = 1 (combined output of Tap A and B)
\(\frac{1}{48} t + \frac{27}{36}= 1\)
\(\frac{1}{48} t = 1 - \frac{3}{4}\)
\(\frac{1}{48} t = \frac{1}{4}\)

t = 12 minutes
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Re: Tap A can fill a tank in 36 minutes, Tap B can fill the same [#permalink]

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conty911 wrote:
Tap A can fill a tank in 36 minutes, Tap B can fill the same tank in 48 minutes. If they are opened simultaneously, at what time tap B (keep tap A running) can be stopped so that the tank can be filled completely filled in 27 minutes.


Let the volume be = 144

Efficiency of A = 4
Efficiency of B = 3
Combinedd efficiency of A & B = 7

7*( 27 - t ) + 4t = 144

189 -7t + 4t = 144

Or, 3t = 45

So, t = 15

Thus tap B must be stopped after 12 ( ie, 27 - 15) minutes
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Re: Tap A can fill a tank in 36 minutes, Tap B can fill the same [#permalink]

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Re: Tap A can fill a tank in 36 minutes, Tap B can fill the same [#permalink]

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New post 12 Feb 2018, 21:21
[quote="conty911"]Tap A can fill a tank in 36 minutes, Tap B can fill the same tank in 48 minutes. If they are opened simultaneously, at what time tap B (keep tap A running) can be stopped so that the tank can be filled completely filled in 27 minutes.

A. 8
B. 12
C. 20
D. 30
E. 36




Ans. Let the volume be = 144

Efficiency of A = 4
Efficiency of B = 3

Tap A will run for 27 minutes so 27*4 = 108 units done
Remaining units will be done by B that is 36/3 = 12 minutes
Tap B will work for 12 minutes.
Re: Tap A can fill a tank in 36 minutes, Tap B can fill the same   [#permalink] 12 Feb 2018, 21:21
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Tap A can fill a tank in 36 minutes, Tap B can fill the same

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