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A tank has both an inlet pipe and an outlet pipe. Working

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A tank has both an inlet pipe and an outlet pipe. Working  [#permalink]

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New post Updated on: 21 Jan 2014, 04:21
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A tank has both an inlet pipe and an outlet pipe. Working alone, the inlet pipe can fill up the tank in 5 hours. Working alone, the outlet pipe can empty out the tank in 15 hours. If it is desired that the tank should be filled, from empty, exactly 6 hours after the inlet pipe is turned on at 9:30am, then at what time should the outlet pipe be opened ?

A. 10:00am
B. 10:45am
C. 12:00pm
D. 12:30pm
E. 1:30pm

Originally posted by guerrero25 on 20 Jan 2014, 08:24.
Last edited by guerrero25 on 21 Jan 2014, 04:21, edited 1 time in total.
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Re: A tank has both an inlet pipe and an outlet pipe. Working  [#permalink]

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New post 20 Jan 2014, 08:47
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guerrero25 wrote:
A tank has both an inlet pipe and an outlet pipe. Working alone, the inlet pipe can fill up the tank in 5 hours. Working alone, the outlet pipe can empty out the tank in 15 hours. If it is desired that the tank should be filled, from empty, exactly 6 hours after the inlet pipe is turned on at 9:30am, then at what time should the outlet pipe be opened ?

A) 10:00am

B) 10:45am

C) 12:00pm

D) 12:30pm

E) 1:30pm


I do not have the OA with me right now .


In 6 hours the inlet pipe will pump in water equal to 6*1/5 = 6/5 of the pool. So, 1/5 more than necessary, which should be compensated by the outlet pipe. To pump out 1/5 of the water the outlet pipe needs 15/5 = 3 hours.

Therefore, the outlet pipe should be opened at 9:30am + 6 hours - 3 hours = 12:30pm.

Answer: D.
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Re: A tank has both an inlet pipe and an outlet pipe. Working  [#permalink]

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New post 20 Jan 2014, 23:05
Bunuel wrote:
guerrero25 wrote:
A tank has both an inlet pipe and an outlet pipe. Working alone, the inlet pipe can fill up the tank in 5 hours. Working alone, the outlet pipe can empty out the tank in 15 hours. If it is desired that the tank should be filled, from empty, exactly 6 hours after the inlet pipe is turned on at 9:30am, then at what time should the outlet pipe be opened ?

A) 10:00am

B) 10:45am

C) 12:00pm

D) 12:30pm

E) 1:30pm


I do not have the OA with me right now .


In 6 hours the inlet pipe will pump in water equal to 6*1/5 = 6/5 of the pool. So, 1/5 more than necessary, which should be compensated by the outlet pipe. To pump out 1/5 of the water the outlet pipe needs 15/5 = 3 hours.

Therefore, the outlet pipe should be opened at 9:30am + 6 hours - 3 hours = 12:30pm.

Answer: D.


Bunuel, but to pump out the excess 1/5 of water, should we not use the combined rate (inflow+outflow)? The combined rate would be 10l outflow/hour. So time required will be 10/5 = 2 hours.

Therefore, the outlet pipe should be opened at 9:30am + 6 hours - 2 hours = 1:30pm. Any mistake here?
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Re: A tank has both an inlet pipe and an outlet pipe. Working  [#permalink]

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New post 20 Jan 2014, 23:45
2
Let us say that the capacity of the tank is 30 liters

Inlet --- 6 liters per hour
Outlet - 2 liters per hour

Let us say it should be turned on after x hours. Total time taken to fill 6 hours

6x + (4)(6-x) = 30
6x + 24 - 4x = 30
2x = 6
x = 3
So it should be opened after 3 hours i.e. 12:30 am
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Re: A tank has both an inlet pipe and an outlet pipe. Working  [#permalink]

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New post 21 Jan 2014, 02:43
HKHR wrote:
Bunuel wrote:
guerrero25 wrote:
A tank has both an inlet pipe and an outlet pipe. Working alone, the inlet pipe can fill up the tank in 5 hours. Working alone, the outlet pipe can empty out the tank in 15 hours. If it is desired that the tank should be filled, from empty, exactly 6 hours after the inlet pipe is turned on at 9:30am, then at what time should the outlet pipe be opened ?

A) 10:00am

B) 10:45am

C) 12:00pm

D) 12:30pm

E) 1:30pm


I do not have the OA with me right now .


In 6 hours the inlet pipe will pump in water equal to 6*1/5 = 6/5 of the pool. So, 1/5 more than necessary, which should be compensated by the outlet pipe. To pump out 1/5 of the water the outlet pipe needs 15/5 = 3 hours.

Therefore, the outlet pipe should be opened at 9:30am + 6 hours - 3 hours = 12:30pm.

Answer: D.


Bunuel, but to pump out the excess 1/5 of water, should we not use the combined rate (inflow+outflow)? The combined rate would be 10l outflow/hour. So time required will be 10/5 = 2 hours.

Therefore, the outlet pipe should be opened at 9:30am + 6 hours - 2 hours = 1:30pm. Any mistake here?


Not sure how you got the numbers there. Combined rate is INFLOW of 1/5-1/15=2/15 pool/hour...

We are interested on time needed for outlet pipe to compensate the excess of 1/5 of the pool.
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Re: A tank has both an inlet pipe and an outlet pipe. Working  [#permalink]

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New post 26 Sep 2014, 22:44
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Inlet: 1/5 t/h
Oulet: 1/15 t/h
together working 1/5-1/15=2/15 t/h

2/15*6=12/15 filled, so 3/15 unfilled

3/15:1/15=3 hours of outlet should subtract. 6-3=3 hours

Answer: D
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Re: A tank has both an inlet pipe and an outlet pipe. Working  [#permalink]

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New post 30 May 2016, 13:14
Hi chetan2u,

I am able to get the solution from the following method-
1/5 * t + 2/15 * (6-t) = 1 (Since the tank should be full after 6 hours)
t/5 + 12/15 -2t/15 = 1
12/15 + t/15 = 1
t/15 = 3/15
t=3

However, I want to discuss 1 more approach
Inlet pipe rate= 1/5
outlet pipe rate= 1/15
Combined rate of Inlet and Outlet = 1/5 - 1/15 = 2/15

As, mentioned in the question the tank gets filled in 6 hours.
We can say that Inlet pipe works for 6 hours and
and Inlet = outlet pipe works for x hours

So, I tried to make the equation as

(1/5)*6 + (2/15)*x= What do I need to put on RHS

Can you please assist.

Thanks and Regards,
Prakhar
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A tank has both an inlet pipe and an outlet pipe. Working  [#permalink]

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New post 18 Sep 2016, 00:01
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PrakharGMAT wrote:
Hi chetan2u,

I am able to get the solution from the following method-
1/5 * t + 2/15 * (6-t) = 1 (Since the tank should be full after 6 hours)
t/5 + 12/15 -2t/15 = 1
12/15 + t/15 = 1
t/15 = 3/15
t=3

However, I want to discuss 1 more approach
Inlet pipe rate= 1/5
outlet pipe rate= 1/15
Combined rate of Inlet and Outlet = 1/5 - 1/15 = 2/15

As, mentioned in the question the tank gets filled in 6 hours.
We can say that Inlet pipe works for 6 hours and
and Inlet = outlet pipe works for x hours

So, I tried to make the equation as

(1/5)*6 + (2/15)*x= What do I need to put on RHS

Can you please assist.

Thanks and Regards,
Prakhar

PrakharGMAT

when you say 2/15 it means the combined work of both inlet and outlet. then you cannot consider 1/5 work of inlet for 6 hours since it will overlap with the combined time.

then equation will \(\frac{2}{15}x+\frac{1}{5}(6-x)=1\)(Since the tank should be full after 68 hours)
solving this equation will result \(x=3\).
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Re: A tank has both an inlet pipe and an outlet pipe. Working  [#permalink]

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Re: A tank has both an inlet pipe and an outlet pipe. Working   [#permalink] 06 Oct 2018, 09:19
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