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Pipe leak

by eaakbari » Sun Apr 11, 2010 10:17 pm
A leak in the bottom of a tank can empty the full tan in 8 hr. An inlet pipe fills water at the rate of 6 lits a minute. When the tank is full,the inlet is opened and due to the leak, the tank is empty in 12 hrs.How many liters does the cistern hold?



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by liferocks » Sun Apr 11, 2010 10:30 pm
consider the cistern holds 800x liters of water
so the leak empties 100x/hr and the pipe fills 6*60=360L/hr
so the full tank will be empty in
800x/(100x-360) hr which is 12
solving this we get the capacity of the cistern is 8640 liters
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by shashank.ism » Sun Apr 11, 2010 10:44 pm
eaakbari wrote:A leak in the bottom of a tank can empty the full tank in 8 hr. An inlet pipe fills water at the rate of 6 lits a minute. When the tank is full,the inlet is opened and due to the leak, the tank is empty in 12 hrs.How many liters does the cistern hold?



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Let V lit. be the vol of tank .
so due to leak total volume which came out = (12/8) * V = (3/2)*V lit.
vol. filled by inlet pipe = 6 * 60 * 12 lit.
so 6 * 60 * 12 + V = (3/2)*V --> (1/2)* V = 6 * 60 * 12 --> V = 6*60*12*2 lit. = 8640 lit.
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by eaakbari » Mon Apr 12, 2010 2:21 am
Work done by the inlet in 1 hr= 1/8 -1/12=1/24
Work done by the inlet in i min= (1/24)*(1/60)=1/1440
Therefore, Volume of 1/1440 part=6 lit
Volume of whole=(1440*6) lit=8640 lit.
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by harshavardhanc » Mon Apr 12, 2010 5:01 am
eaakbari wrote:A leak in the bottom of a tank can empty the full tan in 8 hr. An inlet pipe fills water at the rate of 6 lits a minute. When the tank is full,the inlet is opened and due to the leak, the tank is empty in 12 hrs.How many liters does the cistern hold?



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Leak does a -ve work of 12.5 %(1/8), but due to the inlet pipe the -ve becomes 8.33% (1/12)

or the inlet pipe is doing a +ve work of 12.5 - 8.33 = 4.166 % OR 1/24

Therefore, the inlet pipe fills the tank in 24 hrs. Hence, the quantity in 24 hrs = 24 * 60 * 6 = 8640 lts.
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by samirnajeeb » Sun Jan 02, 2011 1:39 am
a leak can empty in 8 hrs but it took 12 hrs to empty ... so it basically emptied 1.5 tank
thus, 0.5 tank was filled by inlet pipe

rate of inlet pipe = 360 ltr/hr
in 12 hrs = 360*12 lts

capacity of tank is double of what inlet pipe emptied = 360*12*2 = 8640 ltrs
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by GMATGuruNY » Sun Jan 02, 2011 4:13 am
eaakbari wrote:A leak in the bottom of a tank can empty the full tan in 8 hr. An inlet pipe fills water at the rate of 6 lits a minute. When the tank is full,the inlet is opened and due to the leak, the tank is empty in 12 hrs.How many liters does the cistern hold?

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The GMAT would provide answer choices, which we could plug in for the volume of the cistern. The correct answer likely would be divisible by 8 and 12.

Answer choice: volume = 8640 liters
Rate of leak = w/t = 8640/8 = 1080 liters per hour.
Rate of inlet = 6 liters per minute = 360 liters per hour.
Combined rate to empty the tank = leak-inlet = 1080-360 = 720 liter per hour.
Time to empty the tank = w/r = 8640/720 = 12 hours. Success!

The correct answer is 8640 liters.
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