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A tank has a leak which would empty the completely filled cistern in 20 hours. If the tank is full of water and a tap is opened which admits 2 liters of water per minute in the tank, the leak now takes 30 hours to empty the tank. How many liters of water does the tank hold?
- a)2400
- b)4500
- c)1200
- d)7200
Correct answer is option 'D'. Can you explain this answer?
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A tank has a leak which would empty the completely filled cistern in 2...
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A tank has a leak which would empty the completely filled cistern in 2...
Given:
- The leak in the tank would empty the completely filled cistern in 20 hours.
- When a tap is opened, it admits 2 liters of water per minute into the tank.
- The leak now takes 30 hours to empty the tank.
To find:
The capacity of the tank in liters.
Assumptions:
- The leak rate is constant throughout.
- The tap remains open for the entire duration.
Step-by-step solution:
Let's assume the capacity of the tank is 'C' liters.
Leak rate:
The leak in the tank can empty the completely filled cistern in 20 hours, so the leak rate is:
Leak rate = C / 20 liters per hour
Tap rate:
The tap admits 2 liters of water per minute into the tank, so the tap rate is:
Tap rate = 2 liters per minute
Combined rate:
When the tap is open, the effective leak rate decreases because the water is being added to the tank. The combined rate is given by:
Combined rate = Leak rate - Tap rate
Time to empty the tank:
With the tap open, it takes 30 hours to empty the tank. The time can be calculated using the combined rate:
30 hours = C / (Leak rate - Tap rate)
Solving the equations:
We have two equations:
1) Leak rate = C / 20
2) 30 = C / (Leak rate - 2)
We can substitute the value of Leak rate from equation 1 into equation 2:
30 = C / (C / 20 - 2)
Simplifying the equation:
30 = C / ((C - 40) / 20)
30 = 20C / (C - 40)
600C - 12000 = 20C
580C = 12000
C = 12000 / 580
C ≈ 20.69
Therefore, the capacity of the tank is approximately 20.69 liters, which can be rounded to 20.69 liters.
- The leak in the tank would empty the completely filled cistern in 20 hours.
- When a tap is opened, it admits 2 liters of water per minute into the tank.
- The leak now takes 30 hours to empty the tank.
To find:
The capacity of the tank in liters.
Assumptions:
- The leak rate is constant throughout.
- The tap remains open for the entire duration.
Step-by-step solution:
Let's assume the capacity of the tank is 'C' liters.
Leak rate:
The leak in the tank can empty the completely filled cistern in 20 hours, so the leak rate is:
Leak rate = C / 20 liters per hour
Tap rate:
The tap admits 2 liters of water per minute into the tank, so the tap rate is:
Tap rate = 2 liters per minute
Combined rate:
When the tap is open, the effective leak rate decreases because the water is being added to the tank. The combined rate is given by:
Combined rate = Leak rate - Tap rate
Time to empty the tank:
With the tap open, it takes 30 hours to empty the tank. The time can be calculated using the combined rate:
30 hours = C / (Leak rate - Tap rate)
Solving the equations:
We have two equations:
1) Leak rate = C / 20
2) 30 = C / (Leak rate - 2)
We can substitute the value of Leak rate from equation 1 into equation 2:
30 = C / (C / 20 - 2)
Simplifying the equation:
30 = C / ((C - 40) / 20)
30 = 20C / (C - 40)
600C - 12000 = 20C
580C = 12000
C = 12000 / 580
C ≈ 20.69
Therefore, the capacity of the tank is approximately 20.69 liters, which can be rounded to 20.69 liters.
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A tank has a leak which would empty the completely filled cistern in 20 hours. If the tank is full of water and a tap is opened which admits 2 liters of water per minute in the tank, the leak now takes 30 hours to empty the tank. How many liters of water does the tank hold?a)2400b)4500c)1200d)7200Correct answer is option 'D'. Can you explain this answer?
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