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A and B together can do a piece of work in 12 days, B and C together can do it in 16 days. All of them started the work together. After working for 5 days, A left. B worked for another 2 days and left. C completed the remaining work after having worked for a total of 13 days. In how many days can C complete the work?
Most Upvoted Answer
A and B together can do a piece of work in 12 days, B and C together c...
Given Information:
- A + B = 1/12 (A and B can do the work in 12 days)
- B + C = 1/16 (B and C can do the work in 16 days)
Calculating Individual Efficiencies:
- Let's assume A's efficiency is 'a', B's efficiency is 'b', and C's efficiency is 'c'.
- From the given information, we have:
- A + B = 1/12
- B + C = 1/16
Calculating A's Efficiency:
- From A + B = 1/12, we have:
- a + b = 1/12
- a = 1/12 - b
Calculating B's Efficiency:
- From B + C = 1/16, we have:
- b + c = 1/16
- b = 1/16 - c
Calculating C's Efficiency:
- Substituting the values of a and b in b = 1/16 - c, we get:
- (1/12 - b) + b = 1/16
- 1/12 = 1/16 + c
- c = 1/12 - 1/16
- c = 1/48
Finding Total Work:
- The total work is represented by 1.
- Therefore, A + B + C = 1/12 + 1/16 + 1/48 = 1/x (Let x be the total days C takes to complete the work)
Solving for x:
- 4x + 3x + x = 48
- 8x = 48
- x = 6
Conclusion:
- C can complete the work alone in 6 days.
- A + B = 1/12 (A and B can do the work in 12 days)
- B + C = 1/16 (B and C can do the work in 16 days)
Calculating Individual Efficiencies:
- Let's assume A's efficiency is 'a', B's efficiency is 'b', and C's efficiency is 'c'.
- From the given information, we have:
- A + B = 1/12
- B + C = 1/16
Calculating A's Efficiency:
- From A + B = 1/12, we have:
- a + b = 1/12
- a = 1/12 - b
Calculating B's Efficiency:
- From B + C = 1/16, we have:
- b + c = 1/16
- b = 1/16 - c
Calculating C's Efficiency:
- Substituting the values of a and b in b = 1/16 - c, we get:
- (1/12 - b) + b = 1/16
- 1/12 = 1/16 + c
- c = 1/12 - 1/16
- c = 1/48
Finding Total Work:
- The total work is represented by 1.
- Therefore, A + B + C = 1/12 + 1/16 + 1/48 = 1/x (Let x be the total days C takes to complete the work)
Solving for x:
- 4x + 3x + x = 48
- 8x = 48
- x = 6
Conclusion:
- C can complete the work alone in 6 days.
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A and B together can do a piece of work in 12 days, B and C together can do it in 16 days. All of them started the work together. After working for 5 days, A left. B worked for another 2 days and left. C completed the remaining work after having worked for a total of 13 days. In how many days can C complete the work?
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A and B together can do a piece of work in 12 days, B and C together can do it in 16 days. All of them started the work together. After working for 5 days, A left. B worked for another 2 days and left. C completed the remaining work after having worked for a total of 13 days. In how many days can C complete the work? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A and B together can do a piece of work in 12 days, B and C together can do it in 16 days. All of them started the work together. After working for 5 days, A left. B worked for another 2 days and left. C completed the remaining work after having worked for a total of 13 days. In how many days can C complete the work? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A and B together can do a piece of work in 12 days, B and C together can do it in 16 days. All of them started the work together. After working for 5 days, A left. B worked for another 2 days and left. C completed the remaining work after having worked for a total of 13 days. In how many days can C complete the work?.
A and B together can do a piece of work in 12 days, B and C together can do it in 16 days. All of them started the work together. After working for 5 days, A left. B worked for another 2 days and left. C completed the remaining work after having worked for a total of 13 days. In how many days can C complete the work? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A and B together can do a piece of work in 12 days, B and C together can do it in 16 days. All of them started the work together. After working for 5 days, A left. B worked for another 2 days and left. C completed the remaining work after having worked for a total of 13 days. In how many days can C complete the work? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A and B together can do a piece of work in 12 days, B and C together can do it in 16 days. All of them started the work together. After working for 5 days, A left. B worked for another 2 days and left. C completed the remaining work after having worked for a total of 13 days. In how many days can C complete the work?.
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