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# A 4000 liter tank, half-full of water is being filled from a pipe with

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Math Expert
Joined: 02 Sep 2009
Posts: 59126
A 4000 liter tank, half-full of water is being filled from a pipe with  [#permalink]

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23 Sep 2019, 21:18
00:00

Difficulty:

55% (hard)

Question Stats:

63% (02:19) correct 37% (02:19) wrong based on 35 sessions

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Competition Mode Question

A 4000 liter tank, half-full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes. At the same time, the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes. How many minutes does it take to fill the tank completely?

A. 8
B. 12
C. 18
D. 24
E. 48

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Re: A 4000 liter tank, half-full of water is being filled from a pipe with  [#permalink]

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Updated on: 23 Sep 2019, 22:05
2
Quote:
A 4000 liter tank, half-full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes. At the same time, the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes. How many minutes does it take to fill the tank completely?

A. 8
B. 12
C. 18
D. 24
E. 48

Filling 1 kl - 2 minutes => 1/2 kl - 1 minute

4000 liter tank is half full....so 2000 liters to fill => 1000 liters every minute is filled up

Losing 1 kl - 4 minutes and 6 minutes from 2 drains

=> From drain 1- 1000/4 liters = 250 liters per minute lost/minute, and from drain 2- 1000/6 liters lost/minute.

=> Total gain = (250-1000/6) = 500/6 liters per minute.

2000 liters ÷ 500/6 liters/minute = 24 minutes - OPTION D
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Originally posted by EncounterGMAT on 23 Sep 2019, 21:56.
Last edited by EncounterGMAT on 23 Sep 2019, 22:05, edited 1 time in total.
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Re: A 4000 liter tank, half-full of water is being filled from a pipe with  [#permalink]

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23 Sep 2019, 22:05
1
A 4000 liter tank, half-full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes. At the same time, the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes. How many minutes does it take to fill the tank completely?

A. 8
B. 12
C. 18
D. 24
E. 48

Rate of filling = 1/2 - 1/4 - 1/6 = 1/12 kl/min
Amount of water left to be filled = 4000/2 = 2000 l = 2kl

Hence time taken to fill the remaining half filled tank = $$2/\frac{1}{12}$$ min
= 24 min

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Re: A 4000 liter tank, half-full of water is being filled from a pipe with  [#permalink]

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23 Sep 2019, 22:22
1
Rate of tap= 1000/2=500/min
Rate of drain 1=1000/4=250
Rate drain 2 = 1000/6 =500/3
Effective rate of filling = 500-250-500/3 = 250/3
So if in 1 min 250/3 liters is added,
Then how many minutes, t, would it take to add 2000 liters
t = 2000/(250/3) = 2000*3/250 = 24 minutes.

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Re: A 4000 liter tank, half-full of water is being filled from a pipe with  [#permalink]

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23 Sep 2019, 22:25
2
A 4000 liter tank, half-full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes. At the same time, the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes. How many minutes does it take to fill the tank completely?

A. 8
B. 12
C. 18
D. 24
E. 48

so we need 2000l to be filled.....in x minutes

going through options by solving (1000/2 -1000/4 - 1000/6)x = 2000 => x = 24

OA:D
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Re: A 4000 liter tank, half-full of water is being filled from a pipe with  [#permalink]

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Updated on: 23 Sep 2019, 23:33
Let's say there is a pipe A and 2 drains B and C.
A fills the tank at the rate 1/2 KL/min, B drains the tank at the rate of 1/4 KL/min and C drains the tank at the rate of 1/6 KL/min.
So, the tank is filled at the rate of 1/2-1/4-1/6 = 1/12 KL/min.
Therefore, 1KL is filled in 12 mins.
The tank is 4000L and half full, so 2KL is filled in 24 mins.
Kudos if you like the explanation.

Originally posted by Msarkar on 23 Sep 2019, 23:25.
Last edited by Msarkar on 23 Sep 2019, 23:33, edited 2 times in total.
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Re: A 4000 liter tank, half-full of water is being filled from a pipe with  [#permalink]

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23 Sep 2019, 23:26
A 4000 liter tank, half-full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes. At the same time, the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes. How many minutes does it take to fill the tank completely?

We have to fill half tank i.e. 2000 ltr
Lets take LCM of 2, 4, and 6 = 12

So we can say that
Pipe 1: fills tank 6 kiloliter in 12 min
Pipe 2: empties 3 kiloliter in 12 min
Pipe 3: empties 2 kiloliter in 12 min

In 12 min the tank fills 1 kiloliter

Therefore to fill 2000 liter it will take 24 min.

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Re: A 4000 liter tank, half-full of water is being filled from a pipe with  [#permalink]

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24 Sep 2019, 00:02
4000 L tank - 2000 L tank needs to be filled.
2000L = 2Kl
inflow speed-outflow speed=speed with which tank is filled
1/2-1/4-1/6=1/12

1 min<--1/12Kl
12 mins<-- 1 kl
24mins<--- 2 Kl
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Re: A 4000 liter tank, half-full of water is being filled from a pipe with  [#permalink]

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24 Sep 2019, 03:54
net flow rate; 1/2-1/4-1/6 ; 1/12
so for 2000 ltrs time taken ; 2000/1000*12 ; 24 mins
IMO D

A 4000 liter tank, half-full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes. At the same time, the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes. How many minutes does it take to fill the tank completely?

A. 8
B. 12
C. 18
D. 24
E. 48
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Re: A 4000 liter tank, half-full of water is being filled from a pipe with  [#permalink]

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24 Sep 2019, 04:38
Quote:
A 4000 liter tank, half-full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes. At the same time, the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes. How many minutes does it take to fill the tank completely?

A. 8
B. 12
C. 18
D. 24
E. 48

capacity: $$4000L = 4KL$$
time to fill: $$\frac{4}{1/2-(1/4+1/6)}=\frac{4}{1/2-(5/12)}=\frac{4}{1/12}=48$$

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Joined: 15 Mar 2019
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Re: A 4000 liter tank, half-full of water is being filled from a pipe with  [#permalink]

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24 Sep 2019, 04:39
D: 24

Rate of loosing = 1/4 + 1/6 => 5/12KL/M
Rate of filling = 1/2 KL/M

2= 1/2*t-(5/12)*t
t=24
Re: A 4000 liter tank, half-full of water is being filled from a pipe with   [#permalink] 24 Sep 2019, 04:39
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