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leaking tank

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by TOPGMAT » Sat Nov 20, 2010 6:44 am
A tank is fitted with a pipe which fills it at 10 L/hr. After 4 hr, a leak develops in the tank. If the leak had developed after 3 hrs instead of 4, it would have taken 2 hrs longer to fill the tank. How long would it take to fill tha tank of capacity 100L if the leakk existed from the begining ?
1) 20
2) 30
3) 15
4) 25
5) 35

OA: later
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by limestone » Sat Nov 20, 2010 7:11 am
Let's call the time to fill the tank in the first scenario ( the leak appeared after 4 hours) is T
The rate of leaking is: A.

In the first scenario :
Water filled: 10*T
Water leaked: A*(T-4)
Volume of the tank is equal to volume filled - volume leaked:
10T - A*(T-4) = T*(10-A) + 4*A

In the second scenario, when time is "T+2":
Water filled: 10*(T+2)
Water leaked: A*{ (T+2) - 3}
Volume of the tank:
10*(T+2) - A*((T+2) - 3) = 10T + 20 - T*A + A = T*(10-A) + A + 20

We used the same tank in both scenarios, thus:
T*(10-A) + 4*A = T*(10-A) + A + 20, or
3*A = 20, or
A = 6.67 L/Hr

If the leak appears from the beginning, the rate of filling water will be:

Fill rate - leak rate = 10 - 6.67 = 3.33

The 100L tank will be filled in: 100/3.33 = 30 hours.

Pick B. Any one has a better approach? Mine is so long.
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by Rahul@gurome » Sat Nov 20, 2010 8:08 am
TOPGMAT wrote:A tank is fitted with a pipe which fills it at 10 L/hr. After 4 hr, a leak develops in the tank. If the leak had developed after 3 hrs instead of 4, it would have taken 2 hrs longer to fill the tank. How long would it take to fill tha tank of capacity 100L if the leakk existed from the begining ?
1) 20
2) 30
3) 15
4) 25
5) 35[/spoiler]
There is a short method. But I guess it'll take a little time to come up with it. Anyway get familiar with it. Might help in future! :)

Say, the leakage rate is x L/hr.
Only the pipe has filling rate = 10 L/hr.
(Pipe + Leakage) effective filling rate = (10 - x) L/hr.

Suppose two tanks A and B with same volume. Assume the first case is for tank A and second case for tank B. Thus, the leak develops after 4 hr in tank A and after 3 hr in tank B. Now the pipe alone has added 40 L to tank A and 30 L to tank B, after that it works with the leakage.

The difference = (40 - 30) L = 10 L
This difference is compensated with a effective filling rate of (10 - x) L/hr in (2 + 1) hrs = 3 hrs. 1 hr is added because in the first case pipe alone worked for 1 hour.

Thus, 10 = 3*(10 - x) => x = 20/3 L/hr.
(Pipe + Leakage) effective filling rate = (10 - x) L/hr. = (10 - 20/3) L/hr. = 10/3 L/hr.

Time required to fill a 100 L tank = 100/(10/3) hrs = 30 hrs.

The correct answer is B.
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by TOPGMAT » Sat Nov 20, 2010 8:22 am
Hi,
Thats the correct answer...
simply put...
after the leak develops..... it takes (1+2hrs longer) i.e 3hrs to fill 10 L... (before it took only 1 hr)
==> 30 hrs to fill 100L.
:-)
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by Rahul@gurome » Sat Nov 20, 2010 8:36 am
TOPGMAT wrote:Hi,
Thats the correct answer...
simply put...
after the leak develops..... it takes (1+2hrs longer) i.e 3hrs to fill 10 L... (before it took only 1 hr)
==> 30 hrs to fill 100L.
:-)
Nice observation! :)
I missed it. We don't need to determine the leakage rate. It was redundant!
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by Deepthi Subbu » Sat Nov 20, 2010 9:04 am
I am still facing difficulties in understanding the problem . Can someone explain by plugging in values?
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by TOPGMAT » Sat Nov 20, 2010 10:03 am
Hi Deepthi,
The best way to solve this problem is to understand the logic. You need not even put no's...

You know the input is coming at 10L/hr...
It is given that if the leak had occurred one hour before.... i.e 10L before,
it would have taken 2hrs longer to fill the tank...
It simply means with the leak present, you now need 3 hrs to fill the same 10L
correlating, 100L = 3*10=30hrs.

Hope it helps..
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by GMATGuruNY » Sat Nov 20, 2010 12:58 pm
TOPGMAT wrote:A tank is fitted with a pipe which fills it at 10 L/hr. After 4 hr, a leak develops in the tank. If the leak had developed after 3 hrs instead of 4, it would have taken 2 hrs longer to fill the tank. How long would it take to fill tha tank of capacity 100L if the leakk existed from the begining ?
1) 20
2) 30
3) 15
4) 25
5) 35

OA: later
Since the pipe fills the tank at a rate of 10 liters/hour:
After 4 hours, 100-40 = 60 liters will be needed to finish filling the tank.
After 3 hours, 100-30 = 70 liters will be needed to finish filling the tank.

Now let's plug in the answer choices, which represent the time to fill the tank if the leak existed from the beginning.

Answer choice D: time with leak = 25 hours.
Rate with leak = 100/25 = 4 liters/hour.
If the leak starts after 4 hours, time to finish = 60/4 = 15 hours, so total time = 4+15 = 19 hours.
If the leak starts after 3 hours, time to finish = 70/4 = 17.5 hours, so total time = 3+17.5 = 20.5 hours.
Difference in time = 20.5-19 = 1.5 hours.
The difference in time needs to be 2 hours. Eliminate D. We can also eliminate A and C -- which are smaller answer choices -- because we need the time to increase.

Answer choice B: time with leak = 30 hours.
Rate with leak = 100/30 = 10/3 liters/hour.
If the leak starts after 4 hours, time to finish = 60/(10/3)= 18 hours, so total time = 4+18 = 22 hours.
If the leak starts after 3 hours, time to finish = 70/(10/3) = 21 hours, so total time = 3+21 = 24 hours.
Difference in time = 24-22 = 2 hours. Success!

The correct answer is B.
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by Deepthi Subbu » Sat Nov 20, 2010 10:17 pm
Hi TOPtheGMAT,

I got confused where it said , when leak happens , it takes 2 hours longer to fill the tank . Since the capacity is unknown, I was not sure if this relates to filling the tank at the rate of 10 L(where 2 hrs get added to the 1 hr) or after it has filled 30 L(where it would be 3 hrs+ 2 hrs to fill the 30 L capacity ) . Your explanation was logical . But any way to interpret questions correctly when we get stuck??

thanks in advance :)

Thanks GMATGuruNY for explaining by plugging in answer choices.
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by TOPGMAT » Sat Nov 20, 2010 10:58 pm
Hi Deepti,
The q stem asks us to find out the time required to fill the tank with the leak present from the begining.
I think you missed this statement.
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by johnnydee963 » Tue Dec 07, 2010 4:49 am
I don't understand why the answer isn't 20, what am I missing?

I would have done this problem like this:

T= time pipe and leak are running
X = rate of leak

10T-XT = 60

10(T+2)-X(T+2)=70

solving for variables, T=12, and X=5. So if the rate of the leak is 5, 10T-5T=100, T=20.

Obviously this is wrong, but I cannot see why. Please help.
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