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# A water tank is fitted with 8 pipes, some of these 8 pipes fill the

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A water tank is fitted with 8 pipes, some of these 8 pipes fill the  [#permalink]

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08 Aug 2019, 11:10
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A water tank is fitted with 8 pipes, some of these 8 pipes fill the tank and others empty the tank. Each of the pipes that fills the tank fills it in 8 hours, while each of the pipes that empties the tank empties it in 6 hours. If all the 8 pipes are kept open when the water tank is full, it takes 6 hours to drain the tank. How many of these 8 pipes fill the tank?

1. 2 pipes
2. 4 pipes
3. 5 pipes
4. 6 pipes
5. 8 pipes

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A water tank is fitted with 8 pipes, some of these 8 pipes fill the  [#permalink]

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08 Aug 2019, 11:57
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Assume the capacity of tank= LCM(6,8)=24units
Inlet pipe can fill 24/8= 3 units every hour.
Outlet pipe can discharge 24/6= 4 units every hour.

Total number of inlet pipes=x
Total number of outlet pipes= 8-x

{(8-x)*4 - 3x}*6= 24
32-4x-3x= 4
x=4

Total number of inlet pipes=4

DisciplinedPrep wrote:
A water tank is fitted with 8 pipes, some of these 8 pipes fill the tank and others empty the tank. Each of the pipes that fills the tank fills it in 8 hours, while each of the pipes that empties the tank empties it in 6 hours. If all the 8 pipes are kept open when the water tank is full, it takes 6 hours to drain the tank. How many of these 8 pipes fill the tank?

1. 2 pipes
2. 4 pipes
3. 5 pipes
4. 6 pipes
5. 8 pipes
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Re: A water tank is fitted with 8 pipes, some of these 8 pipes fill the  [#permalink]

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07 Sep 2019, 03:40
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Bunuel can you explain this please?
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A water tank is fitted with 8 pipes, some of these 8 pipes fill the  [#permalink]

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07 Sep 2019, 20:12
DisciplinedPrep wrote:
A water tank is fitted with 8 pipes, some of these 8 pipes fill the tank and others empty the tank. Each of the pipes that fills the tank fills it in 8 hours, while each of the pipes that empties the tank empties it in 6 hours. If all the 8 pipes are kept open when the water tank is full, it takes 6 hours to drain the tank. How many of these 8 pipes fill the tank?

1. 2 pipes
2. 4 pipes
3. 5 pipes
4. 6 pipes
5. 8 pipes

let x=number of pipes filling tank
6[(8-x)(1/6)-(x)(1/8)]=1→
x=4
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A water tank is fitted with 8 pipes, some of these 8 pipes fill the  [#permalink]

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19 Sep 2019, 10:13
Let x be the no. of pipes that fill the tank. Hence, no. of pipes that empty the tank will be (8-x).
Rate of pipes that fill is 1/8 and rate of pipes that empty the tank is 1/6.

We are given the information that the tank gets emptied in 6 hrs. Rate of tank emptying per hour is 1/6.
Let's form an equation from the above information.

$$1/6*(8-x)- 1/8*(x) = 1/6$$
$$8/6 - x/6 - x/8 = 1/6$$
$$x/6 - x/8 = 1/6 - 8/6$$
$$-14x/48 = -7/6$$
$$-7x/24 = -7/6$$

Solving for x gives, x =4.

Hence, no. of pipes that fill the tank is 4
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Re: A water tank is fitted with 8 pipes, some of these 8 pipes fill the  [#permalink]

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24 Sep 2019, 02:08
given
total pipes = 8
rate of inlet = 1/8
rate of outlet = 1/6
let total volume of tank be 24 ltrs
so rate of filling ; 24/8 ; 3 ltrs/hr and rate of draining ; 24/6 ; 4 ltrs/hr
work done ; rate * time
work = 24
time of drain is 6 hrs
24= (3*a-(4*(8-a)) ) *6
solve for a = 4
IMO B

DisciplinedPrep wrote:
A water tank is fitted with 8 pipes, some of these 8 pipes fill the tank and others empty the tank. Each of the pipes that fills the tank fills it in 8 hours, while each of the pipes that empties the tank empties it in 6 hours. If all the 8 pipes are kept open when the water tank is full, it takes 6 hours to drain the tank. How many of these 8 pipes fill the tank?

1. 2 pipes
2. 4 pipes
3. 5 pipes
4. 6 pipes
5. 8 pipes
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Re: A water tank is fitted with 8 pipes, some of these 8 pipes fill the  [#permalink]

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24 Sep 2019, 10:26
DisciplinedPrep wrote:
A water tank is fitted with 8 pipes, some of these 8 pipes fill the tank and others empty the tank. Each of the pipes that fills the tank fills it in 8 hours, while each of the pipes that empties the tank empties it in 6 hours. If all the 8 pipes are kept open when the water tank is full, it takes 6 hours to drain the tank. How many of these 8 pipes fill the tank?

1. 2 pipes
2. 4 pipes
3. 5 pipes
4. 6 pipes
5. 8 pipes

We can let the number of filling pipes be n, and thus the number of emptying pipes = 8 - n. Since the rate of each filling pipe is ⅛ and that of each emptying pipe is -⅙ and the combined rate of all pipes is -⅙, we can create the equation:

n x ⅛ + (8 - n) x -⅙ = -⅙

Multiplying by 24, we have:

3n - 4(8 - n) = -4

3n - 32 + 4n = -4

7n = 28

n = 4

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Re: A water tank is fitted with 8 pipes, some of these 8 pipes fill the  [#permalink]

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09 Oct 2019, 05:09
DisciplinedPrep wrote:
A water tank is fitted with 8 pipes, some of these 8 pipes fill the tank and others empty the tank. Each of the pipes that fills the tank fills it in 8 hours, while each of the pipes that empties the tank empties it in 6 hours. If all the 8 pipes are kept open when the water tank is full, it takes 6 hours to drain the tank. How many of these 8 pipes fill the tank?

1. 2 pipes
2. 4 pipes
3. 5 pipes
4. 6 pipes
5. 8 pipes

rate*time=distance

pipes: x+y=8… y=8-x

in rate: 1/8
out rate: 1/6

$$\frac{1}{x(1/8)-y(1/6)}=-6…\frac{1}{x/8-(8-x/6)}=-6…\frac{1}{(6x-64+8x)/48}=-6…48=384-84x…x,y=4$$

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Re: A water tank is fitted with 8 pipes, some of these 8 pipes fill the  [#permalink]

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24 Oct 2019, 04:16
ScottTargetTestPrep sir how did you arrive at the combined rate of -1/6?
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Re: A water tank is fitted with 8 pipes, some of these 8 pipes fill the  [#permalink]

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25 Oct 2019, 09:38
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rocky620 wrote:
ScottTargetTestPrep sir how did you arrive at the combined rate of -1/6?

From the sentence "If all the 8 pipes are kept open when the water tank is full, it takes 6 hours to drain the tank.", we understand that when all the pipes are combined, 1/6 of the tank is emptied in one hour. Since the tank is being emptied instead of being filled, the combined rate will be negative. That's how we find the combined rate of -1/6.
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# Scott Woodbury-Stewart

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Re: A water tank is fitted with 8 pipes, some of these 8 pipes fill the  [#permalink]

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29 Oct 2019, 21:48
ScottTargetTestPrep got it sir, thanks.
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Re: A water tank is fitted with 8 pipes, some of these 8 pipes fill the  [#permalink]

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30 Oct 2019, 08:52
Assume capacity of tank be LCM of 6 and 8 = 24L
Now,
- Per hour rate at inlet of tank = 24/8 = 3L
- Per hour rate at outlet of tank = 24/6 = 4L

if both pipes are open together, -1L is per hour decrease in quantity of tank. but given is that tank will get emptied in 6 hours -- means per hour rate should be -4L.

From above we can deduce that if 4 Inlet and 4 outlet pipes are open - tank will get emptied in 6 hours.

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Re: A water tank is fitted with 8 pipes, some of these 8 pipes fill the   [#permalink] 30 Oct 2019, 08:52