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Water flows into an empty tank of 54 liters via 12 small pipes. The ra

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Bunuel
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Water flows into an empty tank of 54 liters via 12 small pipes. The ra [#permalink] New post   12 Dec 2019, 23:15
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Water flows into an empty tank of 54 liters via 12 small pipes. The rate of flow in each pipe is 1 liter per hour. However, water also flows out of the tank via several large pipes at the rate of 1.5 liter per hour per pipe. If the tank is completely full after 12 hours, how many large pipes are there?

A. 2.5
B. 3
C. 4
D. 5
E. 6

M05-09

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Bunuel
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Re: Water flows into an empty tank of 54 liters via 12 small pipes. The ra [#permalink] New post   18 Nov 2021, 03:17
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Water flows into an empty tank of 54 liters via 12 small pipes. The rate of flow in each pipe is 1 liter per hour. However, water also flows out of the tank via several large pipes at the rate of 1.5 liter per hour per pipe. If the tank is completely full after 12 hours, how many large pipes are there?

A. 2.5
B. 3
C. 4
D. 5
E. 6


The tank is full in 12 hours, therefore, the effective inflow has to be \(\frac{54}{12} = 4.5\) liters per hour. Currently our nominal inflow is 12 liters per hour and outflow is unknown. To find the outflow, we need to subtract effective inflow from the nominal inflow. \(12 - 4.5 = 7.5\); We know that each of the large, outgoing pipes has a flow rate of 1.5 liters per hour, therefore, \(\frac{7.5}{1.5} = 5\).


Answer: D
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rajatchopra1994
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Re: Water flows into an empty tank of 54 liters via 12 small pipes. The ra [#permalink] New post   12 Dec 2019, 23:24
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Bunuel wrote:
Water flows into an empty tank of 54 liters via 12 small pipes. The rate of flow in each pipe is 1 liter per hour. However, water also flows out of the tank via several large pipes at the rate of 1.5 liter per hour per pipe. If the tank is completely full after 12 hours, how many large pipes are there?

A. 2.5
B. 3
C. 4
D. 5
E. 6

M05-09


Explanation:

54 liters filled in 12 hours = net fill rate = 4.5 liters per hour.

Small pipes (incoming) 12 pipes at 1 liter each = 12 liters incoming.

Net = incoming (12) minus outgoing (x) = 4.5

Therefore, the outgoing rate = 7.5

At 1.5 per hour per large pipe, 7.5/1.5 = 5 large pipes.

IMO-D
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Re: Water flows into an empty tank of 54 liters via 12 small pipes. The ra [#permalink] New post   12 Dec 2019, 23:42
12 pipes filling with the rate of 1 l/hr means tank will have 12 l in an hour.
=>In 12 hr tank would have 144 l.But there are outflow pipes and they are emptying at the rate of 1.5l/hr . It means 30 l in 12 hours.
=> 144-30x=54
=> X= 3
IMO B

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Re: Water flows into an empty tank of 54 liters via 12 small pipes. The ra [#permalink] New post   Updated on: 13 Dec 2019, 00:02
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12 pipes are filling the tank with the rate of 1 l/hr means tank will have 12 l in an hour.
=>In 12 hrs tank would have 144 l.But there are outflow pipes and they are emptying the tank at the rate of 1.5l/hr . It means water is getting out at the rate of 18 l/12 hours.
=> 144-18x=54
=> X= 5
IMO D
*Did calculation mistake earlier!

Originally posted by AntrikshR on 12 Dec 2019, 23:44.
Last edited by AntrikshR on 13 Dec 2019, 00:02, edited 1 time in total.
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Re: Water flows into an empty tank of 54 liters via 12 small pipes. The ra [#permalink] New post   12 Dec 2019, 23:56
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Total fill up 12 small pipes by 12 hours @1 liter per hour=12*12*1=144 liters
Total amount remained there after 12 hours =54 liters
So, 144-54=90 liters are OUT by some LARGE pipes which are running at 1.50 liters per hour for 12 hours I.e. 18 liters per pipe in that period
So, number of large pipes is 90/18=5.
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Re: Water flows into an empty tank of 54 liters via 12 small pipes. The ra [#permalink] New post   Updated on: 18 Apr 2022, 13:16
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(1 liter of inflow per small pipe * 12 hours to fill the tank * 12 small pipes) - (1,5 liter of outflow per hour per pipe * 12 hours to fill the tank * X number of large pipes) = 54 liters

1*12*12 - 1,5*12x = 54
144 - 18x = 54
18x = 90
x= 5

Originally posted by frombelarus on 18 May 2020, 01:20.
Last edited by frombelarus on 18 Apr 2022, 13:16, edited 1 time in total.
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Re: Water flows into an empty tank of 54 liters via 12 small pipes. The ra [#permalink]
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