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An oil tank can be filled by pipe X in 5 hours and pipe Y in 4 hours, each pump working on its own. When the oil tank is full and the drainage hole is open, the oil is drained in 20 hours.
If initially the tank was empty and someone started the two pumps together but left the drainage hole open, how many hours will it tak for the tank to be filled? (Assume that the rate of drainage is independent of the head)
If initially the tank was empty and someone started the two pumps together but left the drainage hole open, how many hours will it tak for the tank to be filled? (Assume that the rate of drainage is independent of the head)
- a)2.50
- b)1.50
- c)2.00
- d)4.00
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
An oil tank can be filled by pipe X in 5 hours and pipe Y in 4 hours, ...
Pipe X will fill how much in one hour = 1/5 tank
Pipe Y will fill how much in one hour = 1/4 tank
Drainage will drain out how much water in 1 hour = 1/20 tank
∴ Total tank filled in one hour
2/5 tank gets filled in = 1 hour
∴ Full (i) tank gets filled in
= 5/2 = 2.5 hr
Pipe Y will fill how much in one hour = 1/4 tank
Drainage will drain out how much water in 1 hour = 1/20 tank
∴ Total tank filled in one hour
2/5 tank gets filled in = 1 hour
∴ Full (i) tank gets filled in
= 5/2 = 2.5 hr
Most Upvoted Answer
An oil tank can be filled by pipe X in 5 hours and pipe Y in 4 hours, ...
Problem Breakdown
To solve the problem, we first need to determine the rates at which the pipes fill the tank and the rate at which the tank drains.
Filling Rates
- Pipe X fills the tank in 5 hours, so its rate is:
- Rate of X = 1 tank / 5 hours = 1/5 tanks per hour
- Pipe Y fills the tank in 4 hours, so its rate is:
- Rate of Y = 1 tank / 4 hours = 1/4 tanks per hour
Combined Filling Rate
When both pipes are working together, their combined filling rate is:
- Combined Rate = Rate of X + Rate of Y
- Combined Rate = (1/5 + 1/4) tanks per hour
To add these fractions, find a common denominator (20):
- Combined Rate = (4/20 + 5/20) = 9/20 tanks per hour
Draining Rate
The drainage hole drains the tank in 20 hours, so its rate is:
- Rate of Drain = 1 tank / 20 hours = 1/20 tanks per hour
Net Rate Calculation
Now, we calculate the net rate when both pipes are filling and the hole is draining:
- Net Rate = Combined Rate - Drain Rate
- Net Rate = (9/20 - 1/20) = 8/20 = 2/5 tanks per hour
Time to Fill the Tank
To find the time required to fill the tank at the net rate:
- Time = 1 tank / (2/5 tanks per hour)
- Time = 5/2 hours = 2.5 hours
Conclusion
Therefore, the tank will be filled in 2.50 hours, corresponding to option 'A'.
To solve the problem, we first need to determine the rates at which the pipes fill the tank and the rate at which the tank drains.
Filling Rates
- Pipe X fills the tank in 5 hours, so its rate is:
- Rate of X = 1 tank / 5 hours = 1/5 tanks per hour
- Pipe Y fills the tank in 4 hours, so its rate is:
- Rate of Y = 1 tank / 4 hours = 1/4 tanks per hour
Combined Filling Rate
When both pipes are working together, their combined filling rate is:
- Combined Rate = Rate of X + Rate of Y
- Combined Rate = (1/5 + 1/4) tanks per hour
To add these fractions, find a common denominator (20):
- Combined Rate = (4/20 + 5/20) = 9/20 tanks per hour
Draining Rate
The drainage hole drains the tank in 20 hours, so its rate is:
- Rate of Drain = 1 tank / 20 hours = 1/20 tanks per hour
Net Rate Calculation
Now, we calculate the net rate when both pipes are filling and the hole is draining:
- Net Rate = Combined Rate - Drain Rate
- Net Rate = (9/20 - 1/20) = 8/20 = 2/5 tanks per hour
Time to Fill the Tank
To find the time required to fill the tank at the net rate:
- Time = 1 tank / (2/5 tanks per hour)
- Time = 5/2 hours = 2.5 hours
Conclusion
Therefore, the tank will be filled in 2.50 hours, corresponding to option 'A'.
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An oil tank can be filled by pipe X in 5 hours and pipe Y in 4 hours, each pump working on its own. When the oil tank is full and the drainage hole is open, the oil is drained in 20 hours.If initially the tank was empty and someone started the two pumps together but left the drainage hole open, how many hours will it tak for the tank to be filled? (Assume that the rate of drainage is independent of the head)a)2.50b)1.50c)2.00d)4.00Correct answer is option 'A'. Can you explain this answer?
Question Description
An oil tank can be filled by pipe X in 5 hours and pipe Y in 4 hours, each pump working on its own. When the oil tank is full and the drainage hole is open, the oil is drained in 20 hours.If initially the tank was empty and someone started the two pumps together but left the drainage hole open, how many hours will it tak for the tank to be filled? (Assume that the rate of drainage is independent of the head)a)2.50b)1.50c)2.00d)4.00Correct answer is option 'A'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about An oil tank can be filled by pipe X in 5 hours and pipe Y in 4 hours, each pump working on its own. When the oil tank is full and the drainage hole is open, the oil is drained in 20 hours.If initially the tank was empty and someone started the two pumps together but left the drainage hole open, how many hours will it tak for the tank to be filled? (Assume that the rate of drainage is independent of the head)a)2.50b)1.50c)2.00d)4.00Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An oil tank can be filled by pipe X in 5 hours and pipe Y in 4 hours, each pump working on its own. When the oil tank is full and the drainage hole is open, the oil is drained in 20 hours.If initially the tank was empty and someone started the two pumps together but left the drainage hole open, how many hours will it tak for the tank to be filled? (Assume that the rate of drainage is independent of the head)a)2.50b)1.50c)2.00d)4.00Correct answer is option 'A'. Can you explain this answer?.
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