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A leak in the bottom of a tank can empty the full tank in 6 hours. 26 Mar 2019, 21:33
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C
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76% (02:42) correct 24% (03:00) wrong based on 311 sessions

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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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C
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A leak in the bottom of a tank can empty the full tank in 6 hours. 26 Mar 2019, 21:44
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DisciplinedPrep
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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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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A leak in the bottom of a tank can empty the full tank in 6 hours. 27 Mar 2019, 14:41
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DisciplinedPrep
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 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
C
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A leak in the bottom of a tank can empty the full tank in 6 hours. 27 Mar 2019, 00:23
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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. 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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A leak in the bottom of a tank can empty the full tank in 6 hours. 31 Mar 2019, 00:48
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DisciplinedPrep
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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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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A leak in the bottom of a tank can empty the full tank in 6 hours. 02 Apr 2019, 19:06
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DisciplinedPrep
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
Show more

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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A leak in the bottom of a tank can empty the full tank in 6 hours. 13 Aug 2025, 15:35
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