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Two inlet pipes can fill a cistern in 20 and 24 hours respectively and an outlet pipe can empty 160 gallons of water per hour. All the three pipes working together can fill the empty cistern in 40 hours. What is the capacity (in gallons) of the tank?
- a)1200
- b)2400
- c)3600
- d)1800
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Two inlet pipes can fill a cistern in 20 and 24 hours respectively and...
Let outlet pipe can empty the tank in x hrs.
Given that,
Outlet pipe can empty the tank in 15 hrs.
Given that,
Outlet pipe can empty 160 gallons of water per hour.
⇒ Total capacity of the tank = 160⨯15 = 2400 gallons
Most Upvoted Answer
Two inlet pipes can fill a cistern in 20 and 24 hours respectively and...
Let's assume the capacity of the cistern is C gallons.
Let's calculate the rates at which each pipe fills or empties the cistern:
- The first inlet pipe can fill the cistern in 20 hours, so its filling rate is C/20 gallons per hour.
- The second inlet pipe can fill the cistern in 24 hours, so its filling rate is C/24 gallons per hour.
- The outlet pipe can empty 160 gallons of water per hour, so its emptying rate is 160 gallons per hour.
Now, let's calculate the combined filling rate of both inlet pipes:
Combined filling rate = C/20 + C/24 gallons per hour
According to the given information, when all three pipes work together, they can fill the empty cistern in 40 hours. So, the combined filling rate of all three pipes is:
Combined filling rate = C/40 gallons per hour
Since the combined filling rate of both inlet pipes is equal to the combined filling rate of all three pipes, we can equate the two expressions:
C/20 + C/24 = C/40
To solve this equation, we need to find the least common multiple (LCM) of the denominators 20, 24, and 40, which is 120. Multiplying both sides of the equation by 120, we get:
6C + 5C = 3C
11C = 3C
Dividing both sides of the equation by C, we get:
11 = 3
This is not possible, so there must be an error in our calculations. Let's recheck the rates:
The first inlet pipe fills the cistern at a rate of C/20 gallons per hour.
The second inlet pipe fills the cistern at a rate of C/24 gallons per hour.
The outlet pipe empties the cistern at a rate of 160 gallons per hour.
Comparing the rates, we can see that the combined filling rate of both inlet pipes is slower than the emptying rate of the outlet pipe. Therefore, it is not possible for the cistern to ever get filled.
Hence, the given information is not consistent, and we cannot determine the capacity of the tank.
Let's calculate the rates at which each pipe fills or empties the cistern:
- The first inlet pipe can fill the cistern in 20 hours, so its filling rate is C/20 gallons per hour.
- The second inlet pipe can fill the cistern in 24 hours, so its filling rate is C/24 gallons per hour.
- The outlet pipe can empty 160 gallons of water per hour, so its emptying rate is 160 gallons per hour.
Now, let's calculate the combined filling rate of both inlet pipes:
Combined filling rate = C/20 + C/24 gallons per hour
According to the given information, when all three pipes work together, they can fill the empty cistern in 40 hours. So, the combined filling rate of all three pipes is:
Combined filling rate = C/40 gallons per hour
Since the combined filling rate of both inlet pipes is equal to the combined filling rate of all three pipes, we can equate the two expressions:
C/20 + C/24 = C/40
To solve this equation, we need to find the least common multiple (LCM) of the denominators 20, 24, and 40, which is 120. Multiplying both sides of the equation by 120, we get:
6C + 5C = 3C
11C = 3C
Dividing both sides of the equation by C, we get:
11 = 3
This is not possible, so there must be an error in our calculations. Let's recheck the rates:
The first inlet pipe fills the cistern at a rate of C/20 gallons per hour.
The second inlet pipe fills the cistern at a rate of C/24 gallons per hour.
The outlet pipe empties the cistern at a rate of 160 gallons per hour.
Comparing the rates, we can see that the combined filling rate of both inlet pipes is slower than the emptying rate of the outlet pipe. Therefore, it is not possible for the cistern to ever get filled.
Hence, the given information is not consistent, and we cannot determine the capacity of the tank.
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Two inlet pipes can fill a cistern in 20 and 24 hours respectively and an outlet pipe can empty 160 gallons of water per hour. All the three pipes working together can fill the empty cistern in 40 hours. What is the capacity (in gallons) of the tank?a)1200b)2400c)3600d)1800Correct answer is option 'B'. Can you explain this answer?
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