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

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Intern
Joined: 17 Apr 2010
Posts: 33
A 4000 liter tank, half-full of water is being filled from a pipe with  [#permalink]

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26 Apr 2010, 12:45
1
4
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Difficulty:

75% (hard)

Question Stats:

60% (02:23) correct 40% (02:07) wrong based on 122 sessions

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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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Joined: 12 Jan 2010
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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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26 Apr 2010, 13:03
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1
Tank is Half Full, Volume needed for the tank to be full = 1/2 *4000 = 2000L = 2kL

Now Water coming in 1Kl every 2 mins = 3Kl every 6 mins
Water flowing out Drain 1 = 1Kl every 4 mins = 1.5 KL every 6 mins
water flowing out drain 2 = 1 KL every 6 mins

So net Flow every 6 mins = 3 -(1+1.5) = 0.5 KL every 6 minutes

So Time = Volume needed to be full/net flow = 2/0.5 = 4

So 4 intervals of 6 minutes

total time = 4*6 = 24 minutes, option 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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26 Apr 2010, 13:06
3
FYI: I fell right into the trap and can't get to the right solution. Can anyone explain?[/quote]

Incoming rate = 1kiloliter per 2 min that means 1/2 kl/min

Outgoing rate for 1st drain = 1/4 kl/min
for 2nd drain = 1/6 kl/min

relative speed of the drains = 1/2 - (1/4 + 1/6) = 1/12 kl/min = 1000/12 litre/min

we need to fill 2000 more litres

thus 2000 = speed * time
2000 = 1000*t/12
=> t = 24
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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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26 Apr 2010, 13:08
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Daaang.... .....I forgot that the tank was already half full. Careful reading helps, I guess.

Thank you guys anyway........
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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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26 Apr 2010, 13:13
Ok so kilo means a thousand, therefore 1 kiloliter = 1,000 litres. We need 2 kilolitres to fill this tank, since it's already half full.

Think of it per minute (since water drains and comes in constantly)

In: we have: 1,000/2min = 500 litres per minute
Out: we have: 1,000/4 + 1,000/6

Then do: IN - OUT to figure out the net inflow per minute (you get 83.3). Then divide the total number of litres you need (2,000 by that net inflow to get the minutes) - 24 min. Answer 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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27 Sep 2018, 00:15
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Re: A 4000 liter tank, half-full of water is being filled from a pipe with   [#permalink] 27 Sep 2018, 00:15
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