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A Cistern can be filled by an inlet pipe at the rate of 4 litres per minute. A leak in the bottom of a cistern can empty the full tank in 8 hours. When the cistern is full, the inlet is opened and due to the leak, the cistern is empty in 40 hours. How many litres does the cistern hold?
- a)4000 litre
- b)2400 litre
- c)1920 litre
- d)2020 litre
- e)None of the Above
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A Cistern can be filled by an inlet pipe at the rate of 4 litres per m...
Part emptied by the leak in 1 hour = 1/8
part filled by (leak & inlet open) in 1 hour = 1/40
Part filled by the inlet pipe in 1 hour = 1/8 – 1/40 = 1/10
Inlet pipe fills the tank in = 10 hours
Inlet pipe fills water at the rate of 4 litres a minute.
Capacity of Cistern = 10 * 60 * 4 = 2400 litre
part filled by (leak & inlet open) in 1 hour = 1/40
Part filled by the inlet pipe in 1 hour = 1/8 – 1/40 = 1/10
Inlet pipe fills the tank in = 10 hours
Inlet pipe fills water at the rate of 4 litres a minute.
Capacity of Cistern = 10 * 60 * 4 = 2400 litre
Most Upvoted Answer
A Cistern can be filled by an inlet pipe at the rate of 4 litres per m...
Given:
- Rate at which the inlet pipe fills the cistern = 4 litres/minute
- Time taken by the leak to empty the full tank = 8 hours
- Time taken by the leak to empty the cistern when the inlet is open = 40 hours
To find:
The capacity of the cistern in litres
Explanation:
To find the capacity of the cistern, we need to determine the rate at which the leak empties the cistern.
Step 1: Find the rate at which the leak empties the cistern when the inlet is closed.
- Let the rate at which the leak empties the cistern be L litres/hour.
- In 8 hours, the leak empties the full tank, which means it empties L x 8 litres.
- Therefore, L x 8 = capacity of the cistern. [Equation 1]
Step 2: Find the rate at which the leak empties the cistern when the inlet is open.
- The inlet pipe fills the cistern at a rate of 4 litres/minute.
- In 40 hours, the inlet pipe can fill 4 x 60 x 40 = 9600 litres.
- The leak empties the same amount of water in 40 hours.
- Therefore, the leak empties the cistern at a rate of 9600/40 = 240 litres/hour. [Equation 2]
Step 3: Find the capacity of the cistern.
- From Equation 1, we know that L x 8 = capacity of the cistern.
- From Equation 2, we know that L = 240 litres/hour.
- Substituting the value of L in Equation 1, we get 240 x 8 = capacity of the cistern.
- Therefore, the capacity of the cistern is 1920 litres.
Answer:
The cistern holds 1920 litres. Therefore, the correct answer is option (b) 1920 litres.
- Rate at which the inlet pipe fills the cistern = 4 litres/minute
- Time taken by the leak to empty the full tank = 8 hours
- Time taken by the leak to empty the cistern when the inlet is open = 40 hours
To find:
The capacity of the cistern in litres
Explanation:
To find the capacity of the cistern, we need to determine the rate at which the leak empties the cistern.
Step 1: Find the rate at which the leak empties the cistern when the inlet is closed.
- Let the rate at which the leak empties the cistern be L litres/hour.
- In 8 hours, the leak empties the full tank, which means it empties L x 8 litres.
- Therefore, L x 8 = capacity of the cistern. [Equation 1]
Step 2: Find the rate at which the leak empties the cistern when the inlet is open.
- The inlet pipe fills the cistern at a rate of 4 litres/minute.
- In 40 hours, the inlet pipe can fill 4 x 60 x 40 = 9600 litres.
- The leak empties the same amount of water in 40 hours.
- Therefore, the leak empties the cistern at a rate of 9600/40 = 240 litres/hour. [Equation 2]
Step 3: Find the capacity of the cistern.
- From Equation 1, we know that L x 8 = capacity of the cistern.
- From Equation 2, we know that L = 240 litres/hour.
- Substituting the value of L in Equation 1, we get 240 x 8 = capacity of the cistern.
- Therefore, the capacity of the cistern is 1920 litres.
Answer:
The cistern holds 1920 litres. Therefore, the correct answer is option (b) 1920 litres.
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A Cistern can be filled by an inlet pipe at the rate of 4 litres per minute. A leak in the bottom of a cistern can empty the full tank in 8 hours. When the cistern is full, the inlet is opened and due to the leak, the cistern is empty in 40 hours. How many litres does the cistern hold?a)4000 litreb)2400 litrec)1920 litred)2020 litree)None of the AboveCorrect answer is option 'B'. Can you explain this answer?
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