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A cistern has three pipes X, Y and Z. Pipes X and Y can fill it in 3 and 4 h, respectively, while pipe Z can empty the completely filled cistern in 1 h. If the pipes are opened in order at 1:00 pm, 2:00 pm and 3:00 pm, respectively, at what time will the cistern be empty?
- a)6 : 15 pm
- b)5 : 12 pm
- c)8 : 12 pm
- d)6 : 35 pm
- e)7 : 12 pm
Correct answer is option 'B'. Can you explain this answer?
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A cistern has three pipes X, Y and Z. Pipes X and Y can fill it in 3 a...
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A cistern has three pipes X, Y and Z. Pipes X and Y can fill it in 3 a...
To solve this problem, we need to find the time it takes for the cistern to empty after the three pipes are opened in order.
Let's first calculate the rates at which each pipe fills or empties the cistern:
- Pipe X fills the cistern in 3 hours, so its rate of filling is 1/3 of the cistern per hour.
- Pipe Y fills the cistern in 4 hours, so its rate of filling is 1/4 of the cistern per hour.
- Pipe Z empties the cistern in 1 hour, so its rate of emptying is 1/1 of the cistern per hour.
We can combine these rates to find the net rate at which the cistern is being filled or emptied:
Net rate = (Rate of Pipe X + Rate of Pipe Y) - Rate of Pipe Z
= (1/3 + 1/4) - 1
= (4/12 + 3/12) - 12/12
= 7/12 - 12/12
= -5/12
The negative sign indicates that the cistern is being emptied.
Now, let's calculate the time it takes for the cistern to empty after the three pipes are opened in order. We know that the cistern is initially empty at 1:00 pm when the first pipe is opened.
- Pipe X fills the cistern at a rate of 1/3 of the cistern per hour. So, at 2:00 pm when the second pipe is opened, the cistern is filled by 1/3.
- Pipe Y fills the cistern at a rate of 1/4 of the cistern per hour. So, at 3:00 pm when the third pipe is opened, the cistern is filled by an additional 1/4.
- From 3:00 pm onwards, the cistern is being emptied by pipe Z at a rate of 1/1 of the cistern per hour.
Let's represent the fraction of the cistern filled or emptied at each hour:
- 1:00 pm: 0/12 (cistern is empty)
- 2:00 pm: 4/12 (cistern is filled by 1/3)
- 3:00 pm: 7/12 (cistern is filled by an additional 1/4)
- 4:00 pm: 2/12 (cistern is emptied by 1)
Since the cistern is emptied by 5/12 every hour and there are 2/12 remaining to be emptied, it will take (2/12) / (5/12) = 2/5 hours to empty the cistern completely.
Therefore, the cistern will be empty at 4:00 pm + 2/5 hours = 4:00 pm + 24 minutes = 4:24 pm.
However, none of the provided options match this time. Therefore, there may be an error in the given answer options or the question itself.
Let's first calculate the rates at which each pipe fills or empties the cistern:
- Pipe X fills the cistern in 3 hours, so its rate of filling is 1/3 of the cistern per hour.
- Pipe Y fills the cistern in 4 hours, so its rate of filling is 1/4 of the cistern per hour.
- Pipe Z empties the cistern in 1 hour, so its rate of emptying is 1/1 of the cistern per hour.
We can combine these rates to find the net rate at which the cistern is being filled or emptied:
Net rate = (Rate of Pipe X + Rate of Pipe Y) - Rate of Pipe Z
= (1/3 + 1/4) - 1
= (4/12 + 3/12) - 12/12
= 7/12 - 12/12
= -5/12
The negative sign indicates that the cistern is being emptied.
Now, let's calculate the time it takes for the cistern to empty after the three pipes are opened in order. We know that the cistern is initially empty at 1:00 pm when the first pipe is opened.
- Pipe X fills the cistern at a rate of 1/3 of the cistern per hour. So, at 2:00 pm when the second pipe is opened, the cistern is filled by 1/3.
- Pipe Y fills the cistern at a rate of 1/4 of the cistern per hour. So, at 3:00 pm when the third pipe is opened, the cistern is filled by an additional 1/4.
- From 3:00 pm onwards, the cistern is being emptied by pipe Z at a rate of 1/1 of the cistern per hour.
Let's represent the fraction of the cistern filled or emptied at each hour:
- 1:00 pm: 0/12 (cistern is empty)
- 2:00 pm: 4/12 (cistern is filled by 1/3)
- 3:00 pm: 7/12 (cistern is filled by an additional 1/4)
- 4:00 pm: 2/12 (cistern is emptied by 1)
Since the cistern is emptied by 5/12 every hour and there are 2/12 remaining to be emptied, it will take (2/12) / (5/12) = 2/5 hours to empty the cistern completely.
Therefore, the cistern will be empty at 4:00 pm + 2/5 hours = 4:00 pm + 24 minutes = 4:24 pm.
However, none of the provided options match this time. Therefore, there may be an error in the given answer options or the question itself.
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A cistern has three pipes X, Y and Z. Pipes X and Y can fill it in 3 and 4 h, respectively, while pipe Z can empty the completely filled cistern in 1 h. If the pipes are opened in order at 1:00 pm, 2:00 pm and 3:00 pm, respectively, at what time will the cistern be empty? a)6 : 15 pmb)5 : 12 pmc)8 : 12 pmd)6 : 35 pme)7 : 12 pmCorrect answer is option 'B'. Can you explain this answer?
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A cistern has three pipes X, Y and Z. Pipes X and Y can fill it in 3 and 4 h, respectively, while pipe Z can empty the completely filled cistern in 1 h. If the pipes are opened in order at 1:00 pm, 2:00 pm and 3:00 pm, respectively, at what time will the cistern be empty? a)6 : 15 pmb)5 : 12 pmc)8 : 12 pmd)6 : 35 pme)7 : 12 pmCorrect answer is option 'B'. Can you explain this answer? for Banking Exams 2025 is part of Banking Exams preparation. The Question and answers have been prepared according to the Banking Exams exam syllabus. Information about A cistern has three pipes X, Y and Z. Pipes X and Y can fill it in 3 and 4 h, respectively, while pipe Z can empty the completely filled cistern in 1 h. If the pipes are opened in order at 1:00 pm, 2:00 pm and 3:00 pm, respectively, at what time will the cistern be empty? a)6 : 15 pmb)5 : 12 pmc)8 : 12 pmd)6 : 35 pme)7 : 12 pmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Banking Exams 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cistern has three pipes X, Y and Z. Pipes X and Y can fill it in 3 and 4 h, respectively, while pipe Z can empty the completely filled cistern in 1 h. If the pipes are opened in order at 1:00 pm, 2:00 pm and 3:00 pm, respectively, at what time will the cistern be empty? a)6 : 15 pmb)5 : 12 pmc)8 : 12 pmd)6 : 35 pme)7 : 12 pmCorrect answer is option 'B'. Can you explain this answer?.
A cistern has three pipes X, Y and Z. Pipes X and Y can fill it in 3 and 4 h, respectively, while pipe Z can empty the completely filled cistern in 1 h. If the pipes are opened in order at 1:00 pm, 2:00 pm and 3:00 pm, respectively, at what time will the cistern be empty? a)6 : 15 pmb)5 : 12 pmc)8 : 12 pmd)6 : 35 pme)7 : 12 pmCorrect answer is option 'B'. Can you explain this answer? for Banking Exams 2025 is part of Banking Exams preparation. The Question and answers have been prepared according to the Banking Exams exam syllabus. Information about A cistern has three pipes X, Y and Z. Pipes X and Y can fill it in 3 and 4 h, respectively, while pipe Z can empty the completely filled cistern in 1 h. If the pipes are opened in order at 1:00 pm, 2:00 pm and 3:00 pm, respectively, at what time will the cistern be empty? a)6 : 15 pmb)5 : 12 pmc)8 : 12 pmd)6 : 35 pme)7 : 12 pmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Banking Exams 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cistern has three pipes X, Y and Z. Pipes X and Y can fill it in 3 and 4 h, respectively, while pipe Z can empty the completely filled cistern in 1 h. If the pipes are opened in order at 1:00 pm, 2:00 pm and 3:00 pm, respectively, at what time will the cistern be empty? a)6 : 15 pmb)5 : 12 pmc)8 : 12 pmd)6 : 35 pme)7 : 12 pmCorrect answer is option 'B'. Can you explain this answer?.
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