Two pipes can fill an empty tank in 12 hrs and 18 hrs, respectively. T

Question

Two pipes can fill an empty tank in 12 hrs and 18 hrs, respectively. The pipes are opened simultaneously but it turns out that the tank is defective and has a hole at the bottom. Because of that it takes 48 minutes extra to fill the tank. When the tank is full, the pipes are closed. In how many hours will the tank be emptied due to the hole?

A. 60 hrs
B. 72 hrs
C. 84 hrs
D. 96 hrs
E. 112 hrs

Are You Up For the Challenge: 700 Level Questions

A. 60 hrs
B. 72 hrs
C. 84 hrs
D. 96 hrs
E. 112 hrs

Are You Up For the Challenge: 700 Level Questions

yashikaaggarwal · Accepted Answer

Answer is B. 72 hours 
Take LCM of 12&18=36 litres
Therefore A fills 3litre/hour
And B fills 2litre/hour.
Total 5litre/hour.
And 36litre will be filled in 7.2 hours that is 7 hours and 12 min. (1/5*60 for minutes) -----(1)
Since the tank has leakage it's taking 7hours and 12 minutes+ 48 minutes that is 8 hours to fill tank.
Before tank was filling at the rate of 5litre/hour so it took 7.2 hours. Now we have time we have to draw out how many litres is put into tank per hour which is to be filled in 8 hours. 
36/8=4.5 so the tank is in taking 4.5 litre / hour which will lead the tank to be filled in 8 hours.
Since the tap is not closed or tempered in between. So 0.5 litre per hour minus is the leakage. (3+2-0.5)=4.5 litres. 
Now it takes 1hour to drain 0.5litre from tank.
36litre tank would be drained in 36/0.5 hours. That is 72.
So OA is B option

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lacktutor · Answer

\frac{1}{12} + \frac{1}{18}= \frac{1}{y}

\frac{1}{12} + \frac{1}{18} - \frac{1}{x} = \frac{1}{(y+ 4/5)}

---> x= ???
----------------------------------------------------------------------------------------------------------------------------------
 \frac{3+2}{36}= \frac{1}{y}  -->  y = \frac{36}{5}

---> \frac{1}{12} + \frac{1}{18} - \frac{1}{x} = \frac{1}{(36/5+ 4/5)}= \frac{1}{8}

-->  \frac{1}{x} = \frac{1}{12} + \frac{1}{18} - \frac{1}{8}= \frac{(6+ 4- 9)}{72}

x= 72

Answer (B).

eakabuah · Answer

The two pipes working together will take  \frac{12*18}{(12+18)} = \frac{12*18}{30} = \frac{36}{5} hrs  to fill the tank if there is no leak.
Due to the leak, the time taken,  Tef = \frac{36}{5}+\frac{48}{60} = \frac{36}{5}+\frac{4}{5} = 8 hrs .
But  1/\frac{36}{5}-\frac{1}{Lt}=\frac{1}{8}  where  Lt= time taken for a full tank to be emptied by the leak on the tank.
 \frac{1}{Lt}=\frac{5}{36}-\frac{1}{8} = \frac{10-9}{72} = \frac{1}{72} 
Hence  Lt=72  hours

The answer is B.

CrackverbalGMAT · Answer

Let the capacity of the tank (work to be done) be 360 litres. Although 36 is the LCM of 12 and 18, taking 360 (basically a bigger multiple of 36) is to ensure that we don't have to deal with fractions at a later stage in the problem.

Pipe 1 can fill it in 12 hours, therefore it fills at the rate of 30 litres per hour.
Pipe 2 can fill it in 18 hours, therefore, it fills at the rate of 20 litres per hour.

When they work together, they fill at the rate of 50 litres per hour. If the hole was not present, they would have filled the tank in  \frac{360 }{ 50}  hours i.e. 7.2 hours i.e. 7 hours 12 mins.
With the hole being present at the bottom of the tank, it took 48 minutes more i.e. it took 8 hours. Therefore, the tank must have been filled at an effective rate of 45 litres per hour since  \frac{360 }{ 8}  = 45.

The rate of emptying should hence be 5 litres per hour. To empty 360 litres, the hole will take  \frac{360}{5}  = 72 hours.

The correct answer option is B .

Hope that helps!

ScottTargetTestPrep · Answer

The normal fill rate (i.e, if there is no hole in the tank) is 1/12 + 1/18 = 3/26 + 2/36 = 5/36. Thus, it will take 1/(5/36) = 36/5 hours to fill the tank normally.

Now, let’s let x = the number of hours it takes the full tank to empty due to the hole. Thus, we can create the equation (notice that 48 minutes = 48/60 = 4/5 hour):

1/(5/36 - 1/x) = 36/5 + 4/5

1/(5/36 - 1/x) = 8

5/36 - 1/x = 1/8

Multiplying the equation by 72x, we have:

10x - 72 = 9x

x = 72

Answer: B

SanjaySrini · Answer

Thank you for the solution.

Lipun · Answer

A fills tank in 12 hrs. B fills tank in 18 hrs.

Together they can fill the tank in (12*18)/(12+18) = 36/5 hrs

But because of the leak, they take 48 extra mins to fill the tank. 48 mins = 4/5 hrs

In 1hr they fill 5/36 parts of the tank, so in 4/5 hrs they'll fill 1/9 parts of the tank. This is the extra amount they need to fill because of the leak.

This means 1/9 parts of the tank leaks every 8 hours.

So for the full tank to be empty it will take 9*8 = 72 hours

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Two pipes can fill an empty tank in 12 hrs and 18 hrs, respectively. T

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