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Two pumps are connected to a certain empty container at the same time.

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Bunuel
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Two pumps are connected to a certain empty container at the same time. [#permalink] New post   11 Apr 2021, 19:45
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Two pumps are connected to a certain empty container at the same time. Pump X fills the container water at a constant rate, while pump Y drains water out of the container at a constant rate. The two pumps finish filling the container in four times the duration it would take pump X alone to fill the container. If pump Y alone can empty a whole container in 48 minutes, then how many minutes does it take pump X alone to fill the container?

A. 24
B. 36
C. 48
D. 50
E. 64
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Bunuel
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Re: Two pumps are connected to a certain empty container at the same time. [#permalink] New post   18 Apr 2021, 19:15
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Bunuel wrote:
Two pumps are connected to a certain empty container at the same time. Pump X fills the container water at a constant rate, while pump Y drains water out of the container at a constant rate. The two pumps finish filling the container in four times the duration it would take pump X alone to fill the container. If pump Y alone can empty a whole container in 48 minutes, then how many minutes does it take pump X alone to fill the container?

A. 24
B. 36
C. 48
D. 50
E. 64


Say the rate of pump X is x pool/minute and the rate of pump Y is y pool/minute. The combined rate is therefore {filling rate} - {emptying rate} = x - y pool minute.

The two pumps finish filling the container in four times the duration it would take pump X alone to fill the container: (x - y)*4t = tx --> x = 4/3*y.

Since, pump Y alone can empty a whole container in 48 minutes, then the rate of Y is 1/48 pool/minute (rate is a reciprocal of time).

Hence, x = 4/3*1/48 = 1/36 --> time is a reciprocal of rate, hence it takes 36 minutes pump X alone to fill the container.

Answer: B.

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Hope this helps.
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Re: Two pumps are connected to a certain empty container at the same time. [#permalink] New post   11 Apr 2021, 23:58
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Let us suppose pump x takes T hrs to fill the container

We know tank y empties it in 48 minute (48/60=4/5 hrs)

tank is filled in 4T hrs when both operations happened

so, 4T/T-4T/(4/5)=1

T=3/5=36 mins, Option B should be right choice
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Re: Two pumps are connected to a certain empty container at the same time. [#permalink] New post   13 Apr 2021, 23:35
Bunuel wrote:
Two pumps are connected to a certain empty container at the same time. Pump X fills the container water at a constant rate, while pump Y drains water out of the container at a constant rate. The two pumps finish filling the container in four times the duration it would take pump X alone to fill the container. If pump Y alone can empty a whole container in 48 minutes, then how many minutes does it take pump X alone to fill the container?

A. 24
B. 36
C. 48
D. 50
E. 64


Two concerns with the question
1. If both the pumps fill the container then the time taken should be less, not more when both pumps are open. Therefore this statement doesn't make sense "The two pumps finish filling the container in four times the duration it would take pump X alone to fill the container."

2. Both pumps will take 36 minutes and Pump x will take 144 mins, which is not in the options.
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Re: Two pumps are connected to a certain empty container at the same time. [#permalink] New post   14 Apr 2021, 01:06
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csingh158 wrote:
Bunuel wrote:
Two pumps are connected to a certain empty container at the same time. Pump X fills the container water at a constant rate, while pump Y drains water out of the container at a constant rate. The two pumps finish filling the container in four times the duration it would take pump X alone to fill the container. If pump Y alone can empty a whole container in 48 minutes, then how many minutes does it take pump X alone to fill the container?

A. 24
B. 36
C. 48
D. 50
E. 64


Two concerns with the question
1. If both the pumps fill the container then the time taken should be less, not more when both pumps are open. Therefore this statement doesn't make sense "The two pumps finish filling the container in four times the duration it would take pump X alone to fill the container."

2. Both pumps will take 36 minutes and Pump x will take 144 mins, which is not in the options.


The above highlighted statement makes sense as Pump X is filling the container and Pump Y is emptying it. This is the reason that when both are open they will take more time to fill up compared to when Pump X is only open.

Solution:
Let rate of pump X = x, rate of pump Y = y, time taken by Pump Y alone to empty the container = 48 minutes, time taken by Pump X alone to fill the container = t =?
Work done = filling the tank or emptying the tank = 1 [Work done is taken as 1 when unknown]

y * 48 = 1 [Emptying the container by pump Y]
=> y = \(\frac{1}{48}\)
x * t = 1 [Filling the container by pump X]
=> x = \(\frac{1}{t}\)
Also,
(x - y) * 4t = 1 [Filling the container when both pumps are open]
=> \((\frac{1}{t} - \frac{1}{48}) * 4t = 1\)
=> 4 - \(\frac{t}{12}\) = 1
=> 3 = \(\frac{t}{12}\)
=> t = 12 * 3 = 36 minutes.

So, correct answer is option B.
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Re: Two pumps are connected to a certain empty container at the same time. [#permalink] New post   14 Apr 2021, 02:01
MarmikUpadhyay wrote:
csingh158 wrote:
Bunuel wrote:
Two pumps are connected to a certain empty container at the same time. Pump X fills the container water at a constant rate, while pump Y drains water out of the container at a constant rate. The two pumps finish filling the container in four times the duration it would take pump X alone to fill the container. If pump Y alone can empty a whole container in 48 minutes, then how many minutes does it take pump X alone to fill the container?

A. 24
B. 36
C. 48
D. 50
E. 64


Two concerns with the question
1. If both the pumps fill the container then the time taken should be less, not more when both pumps are open. Therefore this statement doesn't make sense "The two pumps finish filling the container in four times the duration it would take pump X alone to fill the container."

2. Both pumps will take 36 minutes and Pump x will take 144 mins, which is not in the options.


The above highlighted statement makes sense as Pump X is filling the container and Pump Y is emptying it. This is the reason that when both are open they will take more time to fill up compared to when Pump X is only open.

Solution:
Let rate of pump X = x, rate of pump Y = y, time taken by Pump Y alone to empty the container = 48 minutes, time taken by Pump X alone to fill the container = t =?
Work done = filling the tank or emptying the tank = 1 [Work done is taken as 1 when unknown]

y * 48 = 1 [Emptying the container by pump Y]
=> y = \(\frac{1}{48}\)
x * t = 1 [Filling the container by pump X]
=> x = \(\frac{1}{t}\)
Also,
(x - y) * 4t = 1 [Filling the container when both pumps are open]
=> \((\frac{1}{t} - \frac{1}{48}) * 4t = 1\)
=> 4 - \(\frac{t}{12}\) = 1
=> 3 = \(\frac{t}{12}\)
=> t = 12 * 3 = 36 minutes.

So, correct answer is option B.


Oh yes, I missed that Y is draining the pump.
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Re: Two pumps are connected to a certain empty container at the same time. [#permalink]
14 Apr 2021, 02:01
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