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Three pipes A, B and C can fill a cistern in 6 hours. After working at it together for 2
hours, A and B are closed and C filled it in 7 hours. What is the time taken by C
alone to fill the cistem?
hours, A and B are closed and C filled it in 7 hours. What is the time taken by C
alone to fill the cistem?
Most Upvoted Answer
Three pipes A, B and C can fill a cistern in 6 hours. After working at...
Understanding the Problem
To solve the problem, we first need to determine the rates at which pipes A, B, and C fill the cistern.
Combined Rate of A, B, and C
- The three pipes together can fill the cistern in 6 hours.
- Therefore, their combined rate is 1/6 of the cistern per hour.
Work Done in Two Hours
- When A, B, and C work together for 2 hours, they fill:
- Work done = 2 hours × (1/6) = 1/3 of the cistern.
Remaining Work for Pipe C
- After 2 hours, the remaining work to fill the cistern is:
- 1 - 1/3 = 2/3 of the cistern.
Time Taken by Pipe C
- Pipe C fills the remaining 2/3 of the cistern in 7 hours.
- Therefore, C's rate of work is:
- Rate of C = (2/3) / 7 = 2/21 of the cistern per hour.
Finding the Rates of A and B
- Let the rates for A and B be represented as 'a' and 'b' respectively.
- We know:
- a + b + (2/21) = 1/6 (combined rate).
Calculating A and B's Rate
- Rearranging gives us:
- a + b = 1/6 - 2/21.
- To solve this, we convert to a common denominator (42):
- 1/6 = 7/42, and 2/21 = 4/42.
- Therefore:
- a + b = 7/42 - 4/42 = 3/42 = 1/14.
Finding Time Taken by A Alone
- If a + b = 1/14, we need to express A's contribution.
- The time taken by A alone to fill the cistern can be calculated by:
- Time = 1/a, where a = 1/14 - b.
- By solving further, we can find the time taken by A alone.
In conclusion, once we determine the individual rates of A and B, we can calculate the time taken by C (1/(2/21)) and find the overall filling times.
To solve the problem, we first need to determine the rates at which pipes A, B, and C fill the cistern.
Combined Rate of A, B, and C
- The three pipes together can fill the cistern in 6 hours.
- Therefore, their combined rate is 1/6 of the cistern per hour.
Work Done in Two Hours
- When A, B, and C work together for 2 hours, they fill:
- Work done = 2 hours × (1/6) = 1/3 of the cistern.
Remaining Work for Pipe C
- After 2 hours, the remaining work to fill the cistern is:
- 1 - 1/3 = 2/3 of the cistern.
Time Taken by Pipe C
- Pipe C fills the remaining 2/3 of the cistern in 7 hours.
- Therefore, C's rate of work is:
- Rate of C = (2/3) / 7 = 2/21 of the cistern per hour.
Finding the Rates of A and B
- Let the rates for A and B be represented as 'a' and 'b' respectively.
- We know:
- a + b + (2/21) = 1/6 (combined rate).
Calculating A and B's Rate
- Rearranging gives us:
- a + b = 1/6 - 2/21.
- To solve this, we convert to a common denominator (42):
- 1/6 = 7/42, and 2/21 = 4/42.
- Therefore:
- a + b = 7/42 - 4/42 = 3/42 = 1/14.
Finding Time Taken by A Alone
- If a + b = 1/14, we need to express A's contribution.
- The time taken by A alone to fill the cistern can be calculated by:
- Time = 1/a, where a = 1/14 - b.
- By solving further, we can find the time taken by A alone.
In conclusion, once we determine the individual rates of A and B, we can calculate the time taken by C (1/(2/21)) and find the overall filling times.
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Three pipes A, B and C can fill a cistern in 6 hours. After working at it together for 2hours, A and B are closed and C filled it in 7 hours. What is the time taken by Calone to fill the cistem?
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Three pipes A, B and C can fill a cistern in 6 hours. After working at it together for 2hours, A and B are closed and C filled it in 7 hours. What is the time taken by Calone to fill the cistem? for SSC CHSL 2025 is part of SSC CHSL preparation. The Question and answers have been prepared according to the SSC CHSL exam syllabus. Information about Three pipes A, B and C can fill a cistern in 6 hours. After working at it together for 2hours, A and B are closed and C filled it in 7 hours. What is the time taken by Calone to fill the cistem? covers all topics & solutions for SSC CHSL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three pipes A, B and C can fill a cistern in 6 hours. After working at it together for 2hours, A and B are closed and C filled it in 7 hours. What is the time taken by Calone to fill the cistem?.
Three pipes A, B and C can fill a cistern in 6 hours. After working at it together for 2hours, A and B are closed and C filled it in 7 hours. What is the time taken by Calone to fill the cistem? for SSC CHSL 2025 is part of SSC CHSL preparation. The Question and answers have been prepared according to the SSC CHSL exam syllabus. Information about Three pipes A, B and C can fill a cistern in 6 hours. After working at it together for 2hours, A and B are closed and C filled it in 7 hours. What is the time taken by Calone to fill the cistem? covers all topics & solutions for SSC CHSL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three pipes A, B and C can fill a cistern in 6 hours. After working at it together for 2hours, A and B are closed and C filled it in 7 hours. What is the time taken by Calone to fill the cistem?.
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