An outlet pipe empties a tank which is full in 10 hours. If

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An outlet pipe empties a tank which is full in 10 hours. If [#permalink]

05 May 2010, 22:22

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An outlet pipe empties a tank which is full in 10 hours. If the inlet pipe is kept open, which lets water in at the rate of 8 litres/min then outlet pipe would take 6 hours longer. Find the capacity of the tank.

A. 8600 litres
B. 200 litres
C. 12800 litres
D. 11200 litres
E. 13200 litres

[Reveal] Spoiler: OA

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Re: Pipes and cisterns [#permalink]

05 May 2010, 23:23

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vigneshpandi wrote:

I have one more question from Pipes.

An outlet pipe empties a tank which is full in 10 hours. If the inlet pipe is kept open, which lets water in at the rate of 8 litres/min then outlet pipe would take 6 hours longer. Find the capacity of the tank.

A. 8600 litres
B. 200 litres
C. 12800 litres
D. 11200 litres
E. 13200 litres

Let the rate of outlet pipe be x liters/hour;
Rate of inlet pipe is 8 litres/min, or 8*60 = 480 liters/hour;
Net outflow rate when both pipes operate would be x-480 liters/hour.

Capacity of the tank = x*10 hours = (x-480)*(10+6) hours

10x=(x-480)*16 --> x=1280 --> capacity = 10x = 12800 liters.

Answer: C.
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Re: Pipes and cisterns [#permalink]

06 May 2010, 07:45

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Hi,

Time to empty the tank with outlet pipe open = 10 hrs
Time when both inlet and outlet is open =10+6 = 16

So time went up by 60% or is 8/5 of original time. So outflow of water is down by 5/8

Let rate of outlet pipe = x

So new flow is 5/8 of original flow

5x/8 = x - 8

solve this x = 64/3

So volume = 64/3*10*60 = 12800 L
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Re: Pipes and cisterns [#permalink]

29 Sep 2010, 11:27

Rate at which the outlet pipe pumps out water: x Ltr in 10 hours: (x/600) Ltr/min
Rate at which the inlet pipe pumps in water: 8 Ltr/min

Rate at which the tank will be emptied when both inlet and outlet pipe are openend: x Ltr in 16 hours: (x/960) Ltr/min

Outlet rate - Inlet rate = Net outlet rate
(x/600) - 8 = (x/960)

Solving the equation gives x=12800L. Hence C.

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Re: Pipes and cisterns [#permalink]

15 Jan 2011, 12:02

outlet pipe worked for extra 6hrs, so it emptied \frac{6}{10} tank extra.
this \frac{3}{5} tank must be filled by inlet pipe.
total liters filled by inlet pipe in 10+6hrs = 8*60*16 liters

let capacity of tank = x
\frac{3*x}{5} = 8*60*16
x = \frac{5*8*60*16}{3}

x = 12800

HTH

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Re: Pipes and cisterns [#permalink]

22 Feb 2011, 13:19

I solved it in a different way.

rate of water flow in outlet pipe = 1/10
rate of water flow in inlet pipe = 1/x
1/10 - 1/x = 1/(10+6)

1/x =6/160

Therefore, in 1 hr 6/160th of the capacity of the tank is let in = 8*60 =480 litres
therefore the complete capacity = 480 * 160 /6 = 12800
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Re: Pipes and cisterns [#permalink]

22 Feb 2011, 13:42

Let the tank's capacity be 'x' liters
Outlet's rate: x/10 l/h
Inlet's rate: 8 l/min= 480 l/h

Outlet takes 16 hours to empty the full tank when inlet is on.

In 16 hours; inlet would have filled: 16*480 = 7680 liters of water

Thus, Outlet pipe empties a total volume of "x+7680" at a rate of x/10 l/h in 16 hours.

R * t = W
(x/10) * 16 = x+7680
16x = 10x+76800
6x=76800
x=76800/6=12800 litres

Ans: "3"
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Re: Pipes and cisterns [#permalink]

22 Feb 2011, 19:56

vigneshpandi wrote:

I have one more question from Pipes.

An outlet pipe empties a tank which is full in 10 hours. If the inlet pipe is kept open, which lets water in at the rate of 8 litres/min then outlet pipe would take 6 hours longer. Find the capacity of the tank.

1)8600 litres
2) 200 litres
3) 12800 litres
4) 11200 litres
5)13200 litres

There are various ways of approaching this problem. Given below is my take.

Whatever water the inlet pipe pumps-in in 16 hrs, outlet pipe pumps out in 6 hrs (since it takes 6 hrs longer when inlet pipe is open for 16 hrs)
If output pipe were to pump out the water in 10 hrs, inlet pump needed to pump in for 16*10/6 = 80/3 hrs
In 80/3 hrs, inlet pipe would pump in 8*60*80/3 = 12800 lts of water (since inlet pipe pumps in at the rate of 8 liters/min or 8*60 liters/hr)
Answer (C)
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Re: Pipes and cisterns [#permalink]

23 Feb 2011, 01:24

v/10 - outlet rate

Inlet rate = 480L/hr

v/10 - 480 = v/16

v( 8-5)/80 = 480 => v = 480 * 80/3 = 16 * 8 * 100

So the answer is C.
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Re: Pipes and cisterns [#permalink] 23 Feb 2011, 01:24

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An outlet pipe empties a tank which is full in 10 hours. If

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