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A leak in the bottom of a tank can empty the full tank in 6 hours.

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A leak in the bottom of a tank can empty the full tank in 6 hours.  [#permalink]

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New post 26 Mar 2019, 21:33
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A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 8 hours. Find the capacity of the tank.

A. 5780 liters
B. 5770 liters
C. 5760 liters
D. 5750 litres
E. 5790 liters

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A leak in the bottom of a tank can empty the full tank in 6 hours.  [#permalink]

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New post 26 Mar 2019, 21:44
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DisciplinedPrep wrote:
A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 8 hours. Find the capacity of the tank.

A. 5780 liters
B. 5770 liters
C. 5760 liters
D. 5750 litres
E. 5790 liters


Leak empties 1 tank in 6 hrs. So rate of work of leak = -1/6 (because it is negative work)

Inlet + leak empty the tank in 8 hrs. So rate of inlet + rate of leak = -1/8 (again overall work is negative)

Rate of inlet - 1/6 = -1/8
Rate of inlet = (1/24)th tank per hour

Time taken to fill the tank by the inlet = 24 hrs

Rate of inlet = 4 lts per min = 4*60 lts per hour = 240 lts per hour

Volume of water filled in 24 hrs = 240 * 24 = 5760 lts = Capacity of the tank

Answer (C)
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Re: A leak in the bottom of a tank can empty the full tank in 6 hours.  [#permalink]

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New post 27 Mar 2019, 00:23
I need a better formula to solve this problem. Anyone who can help?

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A leak in the bottom of a tank can empty the full tank in 6 hours.  [#permalink]

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New post 27 Mar 2019, 14:41
1
DisciplinedPrep wrote:
A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 8 hours. Find the capacity of the tank.

A. 5780 liters
B. 5770 liters
C. 5760 liters
D. 5750 litres
E. 5790 liters


a leak that can empty 1 full tank in 6 hours
can empty 4/3 of a filling tank in 8 hours
thus, in eight hours, the inlet pipe fills 1/3 of the tank
so 1/3 tank capacity=8 hours*60 minutes*4 liters=1920 liters
and total tank capacity=3*1920=5760 liters
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Re: A leak in the bottom of a tank can empty the full tank in 6 hours.  [#permalink]

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New post 29 Mar 2019, 00:52
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Let the capacity of tank be 'x' liters.
Inflow (inlet pipe): 240 liters per hour
Outflow (Leak): x/6 liters per hour
Net Outflow (Outflow - Inflow): (x/6 - 240) liters per hour
Total outflow in 8 hours: 8(x/6 - 240) liters which is all the water in the tank since the tank empties in 8 hours.
Therefore, 8(x/6 - 240) = x.
Thus x=5760 liters. Ans.: C
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Re: A leak in the bottom of a tank can empty the full tank in 6 hours.  [#permalink]

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New post 31 Mar 2019, 00:48
DisciplinedPrep wrote:
A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 8 hours. Find the capacity of the tank.

A. 5780 liters
B. 5770 liters
C. 5760 liters
D. 5750 litres
E. 5790 liters


net effective time it will take to empty the tank ; 1/6-1/8 ; 1/24 hrs or says 24 hrs
and inlet rate ; 4 ltrs per min; 4*60 ; 240 ltrs per min
so capacity of tank ; 240*24 ; 5760 ltrs
IMO C
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Re: A leak in the bottom of a tank can empty the full tank in 6 hours.  [#permalink]

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New post 02 Apr 2019, 19:06
1
DisciplinedPrep wrote:
A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 8 hours. Find the capacity of the tank.

A. 5780 liters
B. 5770 liters
C. 5760 liters
D. 5750 litres
E. 5790 liters


We can let N = the number of liters of water in the tank when it’s full. Therefore, the rate of the leak (without any inlet pipe filling the tank) is N/(60 x 6) = N/360 liters per minute. However, with the inlet pipe filling the tank at 4 liters per minute, the rate of the leak is N/(60 x 8) = N/480 liters per minute. Therefore, we can create the equation:

N/360 - 4 = N/480

Multiply both sides by 1440, we have:

4N - 5760 = 3N

N = 5760

Answer: C
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Re: A leak in the bottom of a tank can empty the full tank in 6 hours.   [#permalink] 02 Apr 2019, 19:06
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