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There is a leak in the bottom of a tank which can empty a

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Director
Joined: 07 Jun 2004
Posts: 614
Location: PA
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There is a leak in the bottom of a tank which can empty a [#permalink]  06 Jan 2005, 16:28
There is a leak in the bottom of a tank which can empty a full tank in 8 hours. When the tank is full a tap is opened into the tank which intakes water at a rate of 6 Liters / hr and the tank is now emptied in 12 hrs. What is the capacity of the tank.
Intern
Joined: 15 Dec 2004
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144 ltr.

lets assume the capacity of the tank is x.

leakage rate = x/8.

after adding 6 liter/hr..total leakage is x+6*12 = x+ 72

leakage rate = (x+72)/12

since leakage rate will remain same

x/8 = (x+72)/12.
solving for x. x = 144 liter.
VP
Joined: 25 Nov 2004
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Re: Rate Problem [#permalink]  06 Jan 2005, 19:06
rxs0005 wrote:
There is a leak in the bottom of a tank which can empty a full tank in 8 hours. When the tank is full a tap is opened into the tank which intakes water at a rate of 6 Liters / hr and the tank is now emptied in 12 hrs. What is the capacity of the tank.

lekage rate of water = x liters per hour
total capacity of the tank = 8x liters
extra water brought in the full tank during 12 hrs = 6 liters * 12 hrs= 72 liters
extra hours taken to take out the water = 4 hours
therefore, water take out rate, = 72 liters/4 hours = 18 liters

water take out rate before and after is equal. x= 18 liters
if the water take out rate is 18, then the total capacity of the tank = 8*18 liters = 144 liters
Director
Joined: 07 Jun 2004
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OA = 144L

good work guys!!
Director
Joined: 21 Sep 2004
Posts: 615
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good explanation guys. thanks..
Intern
Joined: 19 Dec 2004
Posts: 14
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I got 144 ltrs as well. Thanks for the problem.
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5078
Location: Singapore
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Say capacity is x litres

Leak is causing loss of x/8 litres per hour

Tank is being filled at a rate of 6 litres per hour

Tank is now emptied in 12 hours, which means rate of being emptied is x/12 litres per hour
therefore,

x/8-x/12=6
x=144 litres
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