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

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rxs0005
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There is a leak in the bottom of a tank which can empty a [#permalink] New post   06 Jan 2005, 17:28
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.



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Re: There is a leak in the bottom of a tank which can empty a [#permalink] New post   06 Jan 2005, 17:45
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.
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Re: There is a leak in the bottom of a tank which can empty a [#permalink] New post   06 Jan 2005, 20:06
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
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Re: There is a leak in the bottom of a tank which can empty a [#permalink] New post   06 Jan 2005, 20:07
OA = 144L

good work guys!!
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Re: There is a leak in the bottom of a tank which can empty a [#permalink] New post   07 Jan 2005, 08:52
good explanation guys. thanks..
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Re: There is a leak in the bottom of a tank which can empty a [#permalink] New post   27 Mar 2005, 21:52
I got 144 ltrs as well. Thanks for the problem.
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Re: There is a leak in the bottom of a tank which can empty a [#permalink] New post   30 Mar 2005, 19:47
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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Re: There is a leak in the bottom of a tank which can empty a [#permalink]
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