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

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Manager
Joined: 23 Sep 2009
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An outlet pipe empties a tank which is full in 10 hours. If  [#permalink]

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05 May 2010, 21:22
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Difficulty:

55% (hard)

Question Stats:

70% (03:08) correct 30% (03:16) wrong based on 266 sessions

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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

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VP

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05 May 2010, 22:23
5
5
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.

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06 May 2010, 06:45
1
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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29 Sep 2010, 10:27
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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15 Jan 2011, 11:02
1
1
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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22 Feb 2011, 12:19
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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22 Feb 2011, 12:42
2
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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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22 Feb 2011, 18:56
1
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)
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23 Feb 2011, 00:24
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

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

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31 Dec 2013, 14:50
1
vigneshpandi wrote:
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

If it empties the tank in 10 hours it does 1/10 per hour
Now with the inlet pipe open it will take 16 hours, hence in one hour it does 1/16

So the difference is 1/10 - 1/16 = 3/80 work done per hour

Now, we are told that the inlet pipe lets water in at the rate of 8 litres/min or 480 litres per hour

Hence 3/80x = 480

x = 12800

Hope it helps
Cheers!
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An outlet pipe empties a tank which is full in 10 hours. If  [#permalink]

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23 Nov 2014, 22:38
Let the capacity = C

Total vol of water came out of outlet valve in 16hrs = Initial Vol (i.e. C) + Water added through inlet valve (8 l/min) in 16hrs.

C/10 X 16 = C + 480X16

C = 12800
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Re: An outlet pipe empties a tank which is full in 10 hours. If  [#permalink]

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27 Nov 2014, 20:57
Let the capacity of the tank = x

Time ...................... Rate .......................... Capacity

10 ........................... $$\frac{x}{10}$$ ............................ x (This is for outgoing water to empty the tank)

Inlet pipe rate = 8 lts/min = 480 Lts/hr

$$\frac{x}{480}$$ .......................... 480 ........................... x (Time required for Inlet pipe is x/480)

Total water going out of pipe = Water in tank + Water from inlet pipe

$$\frac{x}{10} (10+6) = x + 480 * (10+6)$$

x = 12800

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

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02 Mar 2016, 18:16
so basically, the pipe needs 6 hours to remove the additional water.
the total additional water is 8l/min * 60 = 480 liters/hour. 16 hours = 480x16.

now, this will be removed in 6 hours..this can only mean that 480x16=6/10 of the total capacity of the tank.
total capacity of the tank = 480x16x10/6 = 12,800 liters
was thinking of backsolving...but it would have taken much more time..
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Joined: 06 Jun 2014
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An outlet pipe empties a tank which is full in 10 hours. If  [#permalink]

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11 Mar 2016, 15:49
The first sentance has modifier issues, that led me to wrong direction and I wasted 30 mints to figure out pretty much noting. I hope not to see such questions again.
Is it just me or someone alse had this problem too?
Manager
Joined: 09 Jun 2015
Posts: 93
Re: An outlet pipe empties a tank which is full in 10 hours. If  [#permalink]

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13 Mar 2016, 07:26
vigneshpandi wrote:
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

Supposing that the inlet pipe takes x hours to fill the empty tank, then (1/10) - (1/x) = 1/16
Solving we get x = 80/3 hours.
Therefore, the capacity of the tank is 80/3 * 60* 8 = 12800 liters.
VP
Joined: 07 Dec 2014
Posts: 1129
An outlet pipe empties a tank which is full in 10 hours. If  [#permalink]

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Updated on: 01 Aug 2018, 15:26
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 c=tank's capacity
if outlet pipe empties 1 tank in 10 hours,
then it will empty 1.6 tanks in 16 hours
thus, inlet pipe must fill .6 tank in 16 hours
.6*c=16*60*8 litres
c=12800 litres
C

Originally posted by gracie on 15 Mar 2016, 13:43.
Last edited by gracie on 01 Aug 2018, 15:26, edited 2 times in total.
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Re: An outlet pipe empties a tank which is full in 10 hours. If  [#permalink]

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25 May 2017, 14:44
vigneshpandi wrote:
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

We can let the capacity of the tank = x liters.

Since it takes 10 hours for the pipe to empty the tank, the rate of the outlet pump is x/10 litres/hour.

The rate of the inlet pipe is 8 litres/min, or 8 x 60 = 480 litres/hour.

However, if the inlet pipe were left open, then it would take 16 hours to empty the tank.

Using the work formula, work = rate x time, we see that the work of the outlet pipe is (x/10)(16) = 16x/10 = 8x/5 and the work of the inlet pipe is (480)(16) = 7680.

We see that there are two actions working against each other: the inlet pipe is letting water in, but the outlet pipe is letting water out. The net amount of work done (emptying the tank of x litres of water) is the difference in these two actions. We can create the following equation to determine x:

8x/5 - 7680 = x

Multiplying the entire equation by 5, we have:

8x - 38,400 = 5x

3x = 38,400

x = 12,800

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

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