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Three pipes A, B and C can fill a cistern in 10 hrs. After working together for 4 hours, C is closed and A and B fill the cistern in 9 hrs. Then find the time in which the cistern can be filled by pipe C?
- a)35 hrs
- b)40 hrs
- c)30 hrs
- d)90 hrs
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Three pipes A, B and C can fill a cistern in 10 hrs. After working to...
A, B and C can fill in 1 hour = 1/10 of the cistern
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A, B, and C can fill in 4 hour= 4/10 =2/5 of the cistern
Remaining part = 1 - 2/5 =3/5 of cistern
3/5 of the cistern is filled by A+B in 9 hours
Therefore, A and B can fill the cistern in 9*5/3 = 15 hrs
Hence in one hour C filled the cistern = 1/10 - 1/15 = 1/30 of the cistern
Hence C can fill the cistern in 30 hrs.
Most Upvoted Answer
Three pipes A, B and C can fill a cistern in 10 hrs. After working to...
Understanding the Problem
To solve the problem, we first need to understand the contribution of each pipe in filling the cistern.
Step 1: Calculate the filling rate of pipes A, B, and C
- Together, pipes A, B, and C fill the cistern in 10 hours.
- This means their combined rate is 1/10 of the cistern per hour.
Step 2: Calculate the work done in the first 4 hours
- In 4 hours, A, B, and C together will fill:
- (1/10) * 4 = 2/5 of the cistern.
Step 3: Remaining work after closing pipe C
- After 4 hours, the amount of cistern left to fill:
- 1 - 2/5 = 3/5 of the cistern.
Step 4: Work done by A and B together
- A and B together fill the remaining 3/5 of the cistern in 9 hours.
- Therefore, their combined rate is:
- (3/5) / 9 = 1/15 of the cistern per hour.
Step 5: Calculate the contribution of pipe C
- Now, we have the rate of A and B together as 1/15.
- Since A, B, and C together fill at 1/10, we can find the rate of C:
- Rate of C = (Rate of A + B + C) - (Rate of A + B)
- Rate of C = (1/10) - (1/15).
Step 6: Finding a common denominator
- The common denominator for 10 and 15 is 30:
- (3/30) - (2/30) = 1/30.
Time taken by pipe C to fill the cistern
- If C fills 1/30 of the cistern in one hour, then it will take 30 hours to fill the entire cistern.
Conclusion
Thus, the time in which pipe C can fill the cistern alone is 30 hours. The correct answer is option 'C'.
To solve the problem, we first need to understand the contribution of each pipe in filling the cistern.
Step 1: Calculate the filling rate of pipes A, B, and C
- Together, pipes A, B, and C fill the cistern in 10 hours.
- This means their combined rate is 1/10 of the cistern per hour.
Step 2: Calculate the work done in the first 4 hours
- In 4 hours, A, B, and C together will fill:
- (1/10) * 4 = 2/5 of the cistern.
Step 3: Remaining work after closing pipe C
- After 4 hours, the amount of cistern left to fill:
- 1 - 2/5 = 3/5 of the cistern.
Step 4: Work done by A and B together
- A and B together fill the remaining 3/5 of the cistern in 9 hours.
- Therefore, their combined rate is:
- (3/5) / 9 = 1/15 of the cistern per hour.
Step 5: Calculate the contribution of pipe C
- Now, we have the rate of A and B together as 1/15.
- Since A, B, and C together fill at 1/10, we can find the rate of C:
- Rate of C = (Rate of A + B + C) - (Rate of A + B)
- Rate of C = (1/10) - (1/15).
Step 6: Finding a common denominator
- The common denominator for 10 and 15 is 30:
- (3/30) - (2/30) = 1/30.
Time taken by pipe C to fill the cistern
- If C fills 1/30 of the cistern in one hour, then it will take 30 hours to fill the entire cistern.
Conclusion
Thus, the time in which pipe C can fill the cistern alone is 30 hours. The correct answer is option 'C'.
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Three pipes A, B and C can fill a cistern in 10 hrs. After working together for 4 hours, C is closed and A and B fill the cistern in 9 hrs. Then find the time in which the cistern can be filled by pipe C?a)35 hrsb)40 hrsc)30 hrsd)90 hrsCorrect answer is option 'C'. Can you explain this answer?
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Three pipes A, B and C can fill a cistern in 10 hrs. After working together for 4 hours, C is closed and A and B fill the cistern in 9 hrs. Then find the time in which the cistern can be filled by pipe C?a)35 hrsb)40 hrsc)30 hrsd)90 hrsCorrect answer is option 'C'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about Three pipes A, B and C can fill a cistern in 10 hrs. After working together for 4 hours, C is closed and A and B fill the cistern in 9 hrs. Then find the time in which the cistern can be filled by pipe C?a)35 hrsb)40 hrsc)30 hrsd)90 hrsCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three pipes A, B and C can fill a cistern in 10 hrs. After working together for 4 hours, C is closed and A and B fill the cistern in 9 hrs. Then find the time in which the cistern can be filled by pipe C?a)35 hrsb)40 hrsc)30 hrsd)90 hrsCorrect answer is option 'C'. Can you explain this answer?.
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