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An outlet pipe empties a tank in 5 hours

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An outlet pipe empties a tank in 5 hours [#permalink]

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New post 02 Apr 2017, 20:23
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Question Stats:

32% (02:11) correct 68% (01:32) wrong based on 105 sessions

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An outlet pipe empties a tank in 5 hours when the tank is 50% full. An inlet pipe, which lets water in at 1/3 liters per min, is opened when the tank was empty and it took 10 hours to fill the tank completely.

Find the capacity of the tank.

A. 10 liters.

B. 100 liters.

C. 1000 liters.

D. 500 liters.

E. 200 liters.

Source: Self-made :-D
[Reveal] Spoiler: OA

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An outlet pipe empties a tank in 5 hours [#permalink]

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New post 02 Apr 2017, 22:38
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RMD007 wrote:
An outlet pipe empties a tank in 5 hours when the tank is 50% full. An inlet pipe, which lets water in at 1/3 liters per min, is opened when the tank was empty and it took 10 hours to fill the tank completely.

Find the capacity of the tank.

A. 10 liters.

B. 100 liters.

C. 1000 liters.

D. 500 liters.

E. 200 liters.

Source: Self-made :-D


let c=tank capacity
outlet pipe empties 1/10 of full tank per hour
inlet pipe fills tank at rate of 20 liters per hour
10 hours*(20 liters-c/10)=c
c=100 liters
B
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An outlet pipe empties a tank in 5 hours [#permalink]

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An outlet pipe empties a tank in 5 hours when the tank is 50% full --> Means it takes 10 hours to empty the tank. In 1 hour, it empties \(\frac{C}{10}\) liters.

Inlet pipe rate is 1/3 liters per minute. ---> per hour \(\frac{1}{3}*60 = 20 liters/hour\)

In 10 hours water from inlet pipe is - 200 liters.

Total water from inlet in 10 hours = Capacity of the tank + Water emptied from outlet in 10 hours

\(200 = C + (\frac{C}{10})*10\)

\(2*C = 200\)

\(C = 100.\)

Choice B.
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Re: An outlet pipe empties a tank in 5 hours [#permalink]

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New post 12 Apr 2017, 21:05
If we consider that both pipes are opened when tank get filled in 10 hours, the capacity of the tank will be 100 liters
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Re: An outlet pipe empties a tank in 5 hours [#permalink]

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New post 06 May 2017, 06:11
RMD007 wrote:
An outlet pipe empties a tank in 5 hours when the tank is 50% full. An inlet pipe, which lets water in at 1/3 liters per min, is opened when the tank was empty and it took 10 hours to fill the tank completely.

Find the capacity of the tank.

A. 10 liters.

B. 100 liters.

C. 1000 liters.

D. 500 liters.

E. 200 liters.

Source: Self-made :-D


In 10 hours, the outlet pipe must have done work of emptying a full tank(say capacity is c).
But what happened is, in 10 hours, we have a full tank. Thus the inlet pipe must have, in ten hours, done the work of filling the tank twice(or in other words, work equal to 2c).

Thus the capacity of the tank is half of what the inlet pipe can do in 10 hours.

\(\frac{1}{2} * 10 * \frac{1}{3} * 60\)

Answer 100(C)
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Re: An outlet pipe empties a tank in 5 hours [#permalink]

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New post 06 May 2017, 08:12
outlet= 50% in 5 h so, 100% in 10 hr
capacity=10x
inlet=1/3 lit per min=1/3*60=20 lit per hr
atq
20*10 - 10x=10x
x=10
capacity= 10*10=100
ans: B
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Re: An outlet pipe empties a tank in 5 hours [#permalink]

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New post 22 Nov 2017, 19:18
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Hi All,

We're told that an outlet pipe empties a tank in 5 hours when the tank is 50% full and that an inlet pipe lets water in at 1/3 liters per min. We're told that the tank starts off empty and took 10 hours to fill the tank. We're asked for the capacity of the tank.

Although the prompt does not state it, we're meant to assume that both pipes are 'working' at the same time. This question gives us two rates, but provides the information in different units. Thus, we have to 'modify' the given information a bit:

Inlet Pipe = 1/3 liters/min = (60 mins)(1/3 liter/min) = 20 liters/hour
Outlet Pipe = 5 hours to remove HALF the tank = (1/2 tank)/5 hours = 1/10 of the tank is emptied per hour

Since it take 10 hours to fill the tank, we have...
(20 liters)(10 hours) = 200 liters going IN
(1/10 tank)(10 hours) = 1 "full tank" going OUT

In algebraic terms, that would be: 200 - X = X
X = 100 liters

Final Answer:
[Reveal] Spoiler:
B


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Re: An outlet pipe empties a tank in 5 hours   [#permalink] 22 Nov 2017, 19:18
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