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M25-09

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Math Expert
Joined: 02 Sep 2009
Posts: 43334

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16 Sep 2014, 00:23
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Difficulty:

35% (medium)

Question Stats:

75% (01:25) correct 25% (01:48) wrong based on 366 sessions

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A draining pipe can empty a pool in 4 hours. On a rainy day, when the pool is full, the draining pipe is opened and the pool is emptied in 6 hours. If rain inflow into the pool is 3 liters per hour, what is the capacity of the pool?

A. $$9$$ liters
B. $$18$$ liters
C. $$27$$ liters
D. $$36$$ liters
E. $$45$$ liters
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
Posts: 43334

Kudos [?]: 139627 [0], given: 12794

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16 Sep 2014, 00:23
Expert's post
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Official Solution:

A draining pipe can empty a pool in 4 hours. On a rainy day, when the pool is full, the draining pipe is opened and the pool is emptied in 6 hours. If rain inflow into the pool is 3 liters per hour, what is the capacity of the pool?

A. $$9$$ liters
B. $$18$$ liters
C. $$27$$ liters
D. $$36$$ liters
E. $$45$$ liters

Let the rate of the draining pipe be $$x$$ liters per hour. Then the capacity of the tank will be $$C=time*rate=4x$$;

Now, when raining, the net outflow is $$x-3$$ liters per hour, and we are told that at this new rate the pool is emptied in 6 hours. So, the capacity (C) of the pool also equals to $$C=time*rate=6(x-3)$$;

Thus we have: $$4x=6(x-3)$$. Solving gives $$x=9$$. Therefore $$C=4x=36$$.

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09 Oct 2014, 04:33
4
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other method
let x be the total capacity
x/4 equal to the drain rate. 3 equals rain inflow
6 hours rain inflow equals 18
x/4=(x+18)/6
6x=4x+72
2x=72
x=36

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Intern
Joined: 13 Jul 2014
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09 Oct 2014, 23:04
7
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Here's how I approached it.

Rain inflow is 3l/hr
After 6 hours it would have filled in 18l
On top of this amount, the pipe would also have to drain the contents of the already filled pool.

We know that draining a filled pool takes 4 hours.
But draining a filled pool + the 18l takes 6 hours, hence it takes 2 hours to drain 18l.

Then do a ratio comparison:
If 18l takes 2 hrs, a filled pool takes 4 hrs.
18:2 = filled pool:4

Hence, filled pool = 36l

It's also easier to just draw a diagram that would look something like this:

|__+18___| 2 hrs
|      x      | 4 hrs
|________|

From the diagram, it is more obvious that x is 36.

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Intern
Joined: 12 Jul 2013
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Schools: HBS '17
GMAT Date: 06-12-2014
GPA: 3.66
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21 Oct 2014, 08:14
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This is how I solved it.

Recall rate eqn: 1/r = 1/r1 + 1/r2

In this case, the rate is negative, hence, 1/r = 1/r1 - 1/r2

i.e. 1/6 = 1/4 - 1/r2

1/r2 = 1/4 - 1/6 = 1/12

Hence r2 = 12

W = RT
C = RT = 3 * 12 = 36
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Manager
Joined: 30 May 2012
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18 Nov 2014, 20:58
dakrownie wrote:
In this case, the rate is negative, hence, 1/r = 1/r1 - 1/r2

May I know why you considered rate to be negative, please? Any examples or resources to that extent is appreciated.

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Intern
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18 Nov 2014, 21:22
Instead of solving question with conventional method, solve it by plugging in the answer choices and out of the given answer choices 36 is the best to pick up.

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Intern
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30 Dec 2014, 02:37
1
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I appreciate all the methods mentioned but they involved a 2-step equation process.

I used this one involving only the rate equation :

Capacity of the pool : x litres
Draining pipe rate : x/4 --- x litres per 4 hours
Rain inflow rate : 3/1 --- 3 litres per 1 hour (negative in this case as draining is emptying and rain is filling the pool)
Group rate : x/6 --- x litres per 6 hours

Usual rate equation : 1/r1 + 1/r2 = 1/r ===> x/4 - 3/1 = x/6 ===> solve for x.

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Senior Manager
Status: Math is psycho-logical
Joined: 07 Apr 2014
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Location: Netherlands
GMAT Date: 02-11-2015
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25 Feb 2015, 13:59
I did it by calculating the reduction in rate, caused by the rain.

So, normally the drain pipe drains the full pool in 4 hours. This means that the draining rate is 1/4.
That rainy day, because the rain was filling the pool while the drain was emptying it, the pool was drained in 6 hours. This means that the draining rate was 1/6.

Now, 1/4-1/6 = 1/12. This must be the rate of the rain inflow. This means that the pool will be totally full in 12 hours (only by the rain).

So, 3 liters per hour is 3*12 = 36. Sounds complicated even to me that I solved it in this way, but sometimes it happens... So, is this way indeed correct?

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Intern
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22 Jul 2015, 03:32
If you follow % efficiency method it will solved in seconds. The outlet pipe can drain the water in 4 days which mean its efficiency is 25% (divide 100 by 4) and when it rains its efficieny is reduced to 16.66% (divide 100 by 6) that means the rain is filling the pool at an efficiency of 8.33% (25%-16.66%). Now from the calculation we can deduce that the rain will take 12 hours to fill the pool (100/8.33%). So just multiply 12 with 3 and get the answer. This approach saves time but one needs to memorise the percentage to fraction conversion table. For example 12.5% =1/8.

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Intern
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02 Jun 2017, 03:16
Tank Capacity=x
Drain rate=x/4 l/hr
Filling rate=3l/hr
Capacity of Tank in 6 hrs= 0
0=x + (3*6) - 6*(x/4)
x=36 litres

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Manager
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01 Aug 2017, 18:21
My 2 cents:
Attachment:

my 2 cents.png [ 4.07 MiB | Viewed 1769 times ]

If you have any question, please let me know & i do like kudos

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Re: M25-09   [#permalink] 01 Aug 2017, 18:21
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