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Pipe A can fill a Tank in 18 Hours, Pipe B can empty a Tank in 12 Hours, Pipe C can fill Tank in 6 Hours. The Tank is already filled up to 1/6 of its capacity. Now Pipe A is opened in the First Hour alone, Pipe B is opened in the Second Hour alone and Pipe C is opened in the Third Hour alone. This cycle is repeated until the Tank gets filled. Then in How many Hours does the rest of Tank gets filled?
- a)15 Hours
- b)18 Hours
- c)20 Hours
- d)24 Hours
- e)None
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Pipe A can fill a Tank in 18 Hours, Pipe B can empty a Tank in 12 Hour...
In First Hour Tank filled = 1/6+1/18
Second Hour = 1/6+1/18-1/12
Third Hour = 1/6+1/18-1/12+1/6 = 11/36 is filled 25/36 is left
From then 3 hours work = 1/18-1/12+1/6 = 5/36
5*3 Hours = 5*5/36 = 25/36
Total = 5*3+3 = 18 Hours
Second Hour = 1/6+1/18-1/12
Third Hour = 1/6+1/18-1/12+1/6 = 11/36 is filled 25/36 is left
From then 3 hours work = 1/18-1/12+1/6 = 5/36
5*3 Hours = 5*5/36 = 25/36
Total = 5*3+3 = 18 Hours
Most Upvoted Answer
Pipe A can fill a Tank in 18 Hours, Pipe B can empty a Tank in 12 Hour...
To find the time it takes to fill the rest of the tank, we need to calculate the rate at which the tank is being filled and then determine the remaining capacity of the tank.
Let's determine the rate at which each pipe fills or empties the tank:
- Pipe A fills the tank in 18 hours, so it fills 1/18 of the tank's capacity in 1 hour.
- Pipe B empties the tank in 12 hours, so it empties 1/12 of the tank's capacity in 1 hour.
- Pipe C fills the tank in 6 hours, so it fills 1/6 of the tank's capacity in 1 hour.
Now, let's calculate the capacity of the tank:
Since the tank is already filled up to 1/6 of its capacity, the remaining capacity is 5/6.
Now, let's calculate the time it takes to fill the remaining capacity of the tank:
- In the first hour, Pipe A fills 1/18 of the tank's capacity.
- In the second hour, Pipe B empties 1/12 of the tank's capacity.
- In the third hour, Pipe C fills 1/6 of the tank's capacity.
After three hours, the net effect is that the tank is filled by (1/18) - (1/12) + (1/6) = 1/18 + 1/12 + 1/6 = (2 + 3 + 6)/36 = 11/36 of its capacity.
So, after three hours, the remaining capacity of the tank is (5/6) - (11/36) = (30/36) - (11/36) = 19/36.
Now, we need to determine the number of cycles required to fill the remaining capacity of the tank:
Since each cycle takes three hours, the number of cycles required is (19/36) / (1/6) = (19/36) * (6/1) = 19/6 = 3.1667.
Since we can't have a fraction of a cycle, we need to round up to the nearest whole number. Therefore, it will take 4 cycles to fill the remaining capacity of the tank.
So, the time it takes to fill the rest of the tank is 4 cycles * 3 hours per cycle = 12 hours.
Therefore, the correct answer is option B) 18 hours.
Let's determine the rate at which each pipe fills or empties the tank:
- Pipe A fills the tank in 18 hours, so it fills 1/18 of the tank's capacity in 1 hour.
- Pipe B empties the tank in 12 hours, so it empties 1/12 of the tank's capacity in 1 hour.
- Pipe C fills the tank in 6 hours, so it fills 1/6 of the tank's capacity in 1 hour.
Now, let's calculate the capacity of the tank:
Since the tank is already filled up to 1/6 of its capacity, the remaining capacity is 5/6.
Now, let's calculate the time it takes to fill the remaining capacity of the tank:
- In the first hour, Pipe A fills 1/18 of the tank's capacity.
- In the second hour, Pipe B empties 1/12 of the tank's capacity.
- In the third hour, Pipe C fills 1/6 of the tank's capacity.
After three hours, the net effect is that the tank is filled by (1/18) - (1/12) + (1/6) = 1/18 + 1/12 + 1/6 = (2 + 3 + 6)/36 = 11/36 of its capacity.
So, after three hours, the remaining capacity of the tank is (5/6) - (11/36) = (30/36) - (11/36) = 19/36.
Now, we need to determine the number of cycles required to fill the remaining capacity of the tank:
Since each cycle takes three hours, the number of cycles required is (19/36) / (1/6) = (19/36) * (6/1) = 19/6 = 3.1667.
Since we can't have a fraction of a cycle, we need to round up to the nearest whole number. Therefore, it will take 4 cycles to fill the remaining capacity of the tank.
So, the time it takes to fill the rest of the tank is 4 cycles * 3 hours per cycle = 12 hours.
Therefore, the correct answer is option B) 18 hours.
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Community Answer
Pipe A can fill a Tank in 18 Hours, Pipe B can empty a Tank in 12 Hour...
In First Hour Tank filled = 1/6+1/18
Second Hour = 1/6+1/18-1/12
Third Hour = 1/6+1/18-1/12+1/6 = 11/36 is filled 25/36 is left
From then 3 hours work = 1/18-1/12+1/6 = 5/36
5*3 Hours = 5*5/36 = 25/36
Total = 5*3+3 = 18 Hours
Second Hour = 1/6+1/18-1/12
Third Hour = 1/6+1/18-1/12+1/6 = 11/36 is filled 25/36 is left
From then 3 hours work = 1/18-1/12+1/6 = 5/36
5*3 Hours = 5*5/36 = 25/36
Total = 5*3+3 = 18 Hours
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Pipe A can fill a Tank in 18 Hours, Pipe B can empty a Tank in 12 Hours, Pipe C can fill Tank in 6 Hours. The Tank is already filled up to 1/6 of its capacity. Now Pipe A is opened in the First Hour alone, Pipe B is opened in the Second Hour alone and Pipe C is opened in the Third Hour alone. This cycle is repeated until the Tank gets filled. Then in How many Hours does the rest of Tank gets filled?a)15 Hoursb)18 Hoursc)20 Hoursd)24 Hourse)NoneCorrect answer is option 'B'. Can you explain this answer?
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Pipe A can fill a Tank in 18 Hours, Pipe B can empty a Tank in 12 Hours, Pipe C can fill Tank in 6 Hours. The Tank is already filled up to 1/6 of its capacity. Now Pipe A is opened in the First Hour alone, Pipe B is opened in the Second Hour alone and Pipe C is opened in the Third Hour alone. This cycle is repeated until the Tank gets filled. Then in How many Hours does the rest of Tank gets filled?a)15 Hoursb)18 Hoursc)20 Hoursd)24 Hourse)NoneCorrect answer is option 'B'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Pipe A can fill a Tank in 18 Hours, Pipe B can empty a Tank in 12 Hours, Pipe C can fill Tank in 6 Hours. The Tank is already filled up to 1/6 of its capacity. Now Pipe A is opened in the First Hour alone, Pipe B is opened in the Second Hour alone and Pipe C is opened in the Third Hour alone. This cycle is repeated until the Tank gets filled. Then in How many Hours does the rest of Tank gets filled?a)15 Hoursb)18 Hoursc)20 Hoursd)24 Hourse)NoneCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Pipe A can fill a Tank in 18 Hours, Pipe B can empty a Tank in 12 Hours, Pipe C can fill Tank in 6 Hours. The Tank is already filled up to 1/6 of its capacity. Now Pipe A is opened in the First Hour alone, Pipe B is opened in the Second Hour alone and Pipe C is opened in the Third Hour alone. This cycle is repeated until the Tank gets filled. Then in How many Hours does the rest of Tank gets filled?a)15 Hoursb)18 Hoursc)20 Hoursd)24 Hourse)NoneCorrect answer is option 'B'. Can you explain this answer?.
Pipe A can fill a Tank in 18 Hours, Pipe B can empty a Tank in 12 Hours, Pipe C can fill Tank in 6 Hours. The Tank is already filled up to 1/6 of its capacity. Now Pipe A is opened in the First Hour alone, Pipe B is opened in the Second Hour alone and Pipe C is opened in the Third Hour alone. This cycle is repeated until the Tank gets filled. Then in How many Hours does the rest of Tank gets filled?a)15 Hoursb)18 Hoursc)20 Hoursd)24 Hourse)NoneCorrect answer is option 'B'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Pipe A can fill a Tank in 18 Hours, Pipe B can empty a Tank in 12 Hours, Pipe C can fill Tank in 6 Hours. The Tank is already filled up to 1/6 of its capacity. Now Pipe A is opened in the First Hour alone, Pipe B is opened in the Second Hour alone and Pipe C is opened in the Third Hour alone. This cycle is repeated until the Tank gets filled. Then in How many Hours does the rest of Tank gets filled?a)15 Hoursb)18 Hoursc)20 Hoursd)24 Hourse)NoneCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Pipe A can fill a Tank in 18 Hours, Pipe B can empty a Tank in 12 Hours, Pipe C can fill Tank in 6 Hours. The Tank is already filled up to 1/6 of its capacity. Now Pipe A is opened in the First Hour alone, Pipe B is opened in the Second Hour alone and Pipe C is opened in the Third Hour alone. This cycle is repeated until the Tank gets filled. Then in How many Hours does the rest of Tank gets filled?a)15 Hoursb)18 Hoursc)20 Hoursd)24 Hourse)NoneCorrect answer is option 'B'. Can you explain this answer?.
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