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A cistern has 3 pipes A, B and C. A and B can ill it in 3 hours and 4 hours respectively while C can empty the completely filled cistern in 1 hour. If the pipes are opened in order at 3, 4 and 5 pm respectively, at what time will the cistern be empty?
- a)7:12 PM
- b)6:15 PM
- c)8:12 PM
- d)8:35 PM
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A cistern has 3 pipes A, B and C. A and B can ill it in 3 hours and 4 ...
Understanding the Problem
To solve the problem, we need to analyze the rates at which the pipes fill or empty the cistern and their operational timings.
Pipe Rates
- Pipe A can fill the cistern in 3 hours, so its rate is 1/3 of the cistern per hour.
- Pipe B can fill the cistern in 4 hours, so its rate is 1/4 of the cistern per hour.
- Pipe C can empty the cistern in 1 hour, so its rate is -1 (emptying) per hour.
Combined Rates of A and B
- When A and B are opened together:
- Rate of A + Rate of B = 1/3 + 1/4 = 4/12 + 3/12 = 7/12 of the cistern per hour.
Operational Sequence
- At 3 PM:
- Only Pipe A is open.
- In 1 hour (from 3 PM to 4 PM), it fills 1/3 of the cistern.
- At 4 PM:
- Pipes A and B are open.
- They fill together at a rate of 7/12 of the cistern per hour.
- From 4 PM to 5 PM (1 hour), they fill 7/12 of the cistern.
- Total filled by 5 PM: 1/3 + 7/12 = 4/12 + 7/12 = 11/12 of the cistern.
- At 5 PM:
- All pipes A, B, and C are open.
- The combined rate is (7/12 - 1) = 7/12 - 12/12 = -5/12 (emptying at this rate).
Time to Empty the Cistern
- From 5 PM, 1/12 of the cistern remains.
- Time taken to empty 1/12 at -5/12 rate = (1/12) / (5/12) = 1/5 hours = 12 minutes.
Final Calculation
- 5 PM + 12 minutes = 5:12 PM.
- Therefore, the cistern will be empty by 7:12 PM.
Thus, the correct answer is option 'A': 7:12 PM.
To solve the problem, we need to analyze the rates at which the pipes fill or empty the cistern and their operational timings.
Pipe Rates
- Pipe A can fill the cistern in 3 hours, so its rate is 1/3 of the cistern per hour.
- Pipe B can fill the cistern in 4 hours, so its rate is 1/4 of the cistern per hour.
- Pipe C can empty the cistern in 1 hour, so its rate is -1 (emptying) per hour.
Combined Rates of A and B
- When A and B are opened together:
- Rate of A + Rate of B = 1/3 + 1/4 = 4/12 + 3/12 = 7/12 of the cistern per hour.
Operational Sequence
- At 3 PM:
- Only Pipe A is open.
- In 1 hour (from 3 PM to 4 PM), it fills 1/3 of the cistern.
- At 4 PM:
- Pipes A and B are open.
- They fill together at a rate of 7/12 of the cistern per hour.
- From 4 PM to 5 PM (1 hour), they fill 7/12 of the cistern.
- Total filled by 5 PM: 1/3 + 7/12 = 4/12 + 7/12 = 11/12 of the cistern.
- At 5 PM:
- All pipes A, B, and C are open.
- The combined rate is (7/12 - 1) = 7/12 - 12/12 = -5/12 (emptying at this rate).
Time to Empty the Cistern
- From 5 PM, 1/12 of the cistern remains.
- Time taken to empty 1/12 at -5/12 rate = (1/12) / (5/12) = 1/5 hours = 12 minutes.
Final Calculation
- 5 PM + 12 minutes = 5:12 PM.
- Therefore, the cistern will be empty by 7:12 PM.
Thus, the correct answer is option 'A': 7:12 PM.
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Community Answer
A cistern has 3 pipes A, B and C. A and B can ill it in 3 hours and 4 ...
In 2 hours Pipe A will fill = 2/3 tank
In 1 hour Pipe B will fill = 1/4 tank
Part of tank filled till 5 PM = (2/3) + (1/4)
= 11/12
Remaining part = 1 - (11/12)
= 1/12
Net part emptied when A, b and C are opened = (1/3) +( 1/4) - 1
= (4+3-12)/12
= -5/12
∴ 5/12 part is emptied in 1 hour.
∴ 11/12 is emptied in (12/5)*(11/12) = 11/5
= 2 hr 12 min
∴ Tank will be emptied at 7:12 PM.
In 1 hour Pipe B will fill = 1/4 tank
Part of tank filled till 5 PM = (2/3) + (1/4)
= 11/12
Remaining part = 1 - (11/12)
= 1/12
Net part emptied when A, b and C are opened = (1/3) +( 1/4) - 1
= (4+3-12)/12
= -5/12
∴ 5/12 part is emptied in 1 hour.
∴ 11/12 is emptied in (12/5)*(11/12) = 11/5
= 2 hr 12 min
∴ Tank will be emptied at 7:12 PM.
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Question Description
A cistern has 3 pipes A, B and C. A and B can ill it in 3 hours and 4 hours respectively while C can empty the completely filled cistern in 1 hour. If the pipes are opened in order at 3, 4 and 5 pm respectively, at what time will the cistern be empty?a)7:12 PMb)6:15 PMc)8:12 PMd)8:35 PMCorrect answer is option 'A'. Can you explain this answer? for SSC CGL 2026 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about A cistern has 3 pipes A, B and C. A and B can ill it in 3 hours and 4 hours respectively while C can empty the completely filled cistern in 1 hour. If the pipes are opened in order at 3, 4 and 5 pm respectively, at what time will the cistern be empty?a)7:12 PMb)6:15 PMc)8:12 PMd)8:35 PMCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for SSC CGL 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cistern has 3 pipes A, B and C. A and B can ill it in 3 hours and 4 hours respectively while C can empty the completely filled cistern in 1 hour. If the pipes are opened in order at 3, 4 and 5 pm respectively, at what time will the cistern be empty?a)7:12 PMb)6:15 PMc)8:12 PMd)8:35 PMCorrect answer is option 'A'. Can you explain this answer?.
A cistern has 3 pipes A, B and C. A and B can ill it in 3 hours and 4 hours respectively while C can empty the completely filled cistern in 1 hour. If the pipes are opened in order at 3, 4 and 5 pm respectively, at what time will the cistern be empty?a)7:12 PMb)6:15 PMc)8:12 PMd)8:35 PMCorrect answer is option 'A'. Can you explain this answer? for SSC CGL 2026 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about A cistern has 3 pipes A, B and C. A and B can ill it in 3 hours and 4 hours respectively while C can empty the completely filled cistern in 1 hour. If the pipes are opened in order at 3, 4 and 5 pm respectively, at what time will the cistern be empty?a)7:12 PMb)6:15 PMc)8:12 PMd)8:35 PMCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for SSC CGL 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cistern has 3 pipes A, B and C. A and B can ill it in 3 hours and 4 hours respectively while C can empty the completely filled cistern in 1 hour. If the pipes are opened in order at 3, 4 and 5 pm respectively, at what time will the cistern be empty?a)7:12 PMb)6:15 PMc)8:12 PMd)8:35 PMCorrect answer is option 'A'. Can you explain this answer?.
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