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Rahul and Rajesh together can complete a piece of work in 12 days, which Rajesh and Ravi together can complete in 16 days. After Rahul has been working at it for 5 days, he leaves and Rajesh takes over for the next 7 days, before he leaves too, and finally Ravi finishes off the remaining work in 13 days. In how many days Ravi alone could have alone done the work?
Correct answer is '24'. Can you explain this answer?
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Rahul and Rajesh together can complete a piece of work in 12 days, wh...
Given information:
- Rahul and Rajesh together can complete a piece of work in 12 days.
- Rajesh and Ravi together can complete the same piece of work in 16 days.
- Rahul works for 5 days, Rajesh works for 7 days, and Ravi finishes the remaining work in 13 days.
Let's assume that the total work is represented by W.
Step 1: Determine the work done by Rahul in 5 days
- Rahul and Rajesh can complete the work in 12 days, so their combined rate of work is 1/12.
- Since Rahul works for 5 days, his work done is (1/12) * 5 = 5/12 of the total work.
- Therefore, the remaining work is (1 - 5/12) = 7/12.
Step 2: Determine the work done by Rajesh in 7 days
- Rajesh and Ravi can complete the work in 16 days, so their combined rate of work is 1/16.
- Since Rajesh works for 7 days, his work done is (1/16) * 7 = 7/16 of the remaining work (7/12).
- Therefore, the remaining work is (7/12 - 7/16) = 14/48 = 7/24.
Step 3: Determine the work done by Ravi in 13 days
- Ravi finishes the remaining work in 13 days, so his work done is (1/13) * (7/24) = 7/312 of the total work.
Step 4: Determine the work done by Ravi in 1 day
- Ravi's work done in 13 days is 7/312 of the total work.
- Therefore, his work done in 1 day is (7/312) * (1/13) = 7/3744 of the total work.
Step 5: Determine the number of days Ravi would take to complete the work alone
- If Ravi's work done in 1 day is 7/3744 of the total work, then he would complete the work in 3744/7 days.
- Simplifying, we get 24 days.
Therefore, Ravi alone could have done the work in 24 days.
- Rahul and Rajesh together can complete a piece of work in 12 days.
- Rajesh and Ravi together can complete the same piece of work in 16 days.
- Rahul works for 5 days, Rajesh works for 7 days, and Ravi finishes the remaining work in 13 days.
Let's assume that the total work is represented by W.
Step 1: Determine the work done by Rahul in 5 days
- Rahul and Rajesh can complete the work in 12 days, so their combined rate of work is 1/12.
- Since Rahul works for 5 days, his work done is (1/12) * 5 = 5/12 of the total work.
- Therefore, the remaining work is (1 - 5/12) = 7/12.
Step 2: Determine the work done by Rajesh in 7 days
- Rajesh and Ravi can complete the work in 16 days, so their combined rate of work is 1/16.
- Since Rajesh works for 7 days, his work done is (1/16) * 7 = 7/16 of the remaining work (7/12).
- Therefore, the remaining work is (7/12 - 7/16) = 14/48 = 7/24.
Step 3: Determine the work done by Ravi in 13 days
- Ravi finishes the remaining work in 13 days, so his work done is (1/13) * (7/24) = 7/312 of the total work.
Step 4: Determine the work done by Ravi in 1 day
- Ravi's work done in 13 days is 7/312 of the total work.
- Therefore, his work done in 1 day is (7/312) * (1/13) = 7/3744 of the total work.
Step 5: Determine the number of days Ravi would take to complete the work alone
- If Ravi's work done in 1 day is 7/3744 of the total work, then he would complete the work in 3744/7 days.
- Simplifying, we get 24 days.
Therefore, Ravi alone could have done the work in 24 days.
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Rahul and Rajesh together can complete a piece of work in 12 days, wh...
Let us assume that the entire work can be completed by Rahul alone, in 'A' number of days, Rajesh alone, in 'B' number of days, and Ravi alone, in 'C' number of days.
So the work done in one day by Rahul, Rajesh and Ravi individually is 1/A, 1/B, 1/C respectively.
As per question,
1/A + 1/B = 1/12
1/B + 1/C = 1/16
and
5/A + 7/B + 13/C =1
or (5/A + 5/B) + (2/B + 2/C) + 11/C = 1
or 5(1/A + 1/B) + 2(1/B + 1/C) + 11/C =1
or 5/12 + 2/16 + 11/C = 1
or C = 24
Hence Ravi can alone do the work in 24 days.
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Rahul and Rajesh together can complete a piece of work in 12 days, which Rajesh and Ravi together can complete in 16 days. After Rahul has been working at it for 5 days, he leaves and Rajesh takes over for the next 7 days, before he leaves too, and finally Ravi finishes off the remaining work in 13 days. In how many days Ravi alone could have alone done the work?Correct answer is '24'. Can you explain this answer?
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Rahul and Rajesh together can complete a piece of work in 12 days, which Rajesh and Ravi together can complete in 16 days. After Rahul has been working at it for 5 days, he leaves and Rajesh takes over for the next 7 days, before he leaves too, and finally Ravi finishes off the remaining work in 13 days. In how many days Ravi alone could have alone done the work?Correct answer is '24'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Rahul and Rajesh together can complete a piece of work in 12 days, which Rajesh and Ravi together can complete in 16 days. After Rahul has been working at it for 5 days, he leaves and Rajesh takes over for the next 7 days, before he leaves too, and finally Ravi finishes off the remaining work in 13 days. In how many days Ravi alone could have alone done the work?Correct answer is '24'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Rahul and Rajesh together can complete a piece of work in 12 days, which Rajesh and Ravi together can complete in 16 days. After Rahul has been working at it for 5 days, he leaves and Rajesh takes over for the next 7 days, before he leaves too, and finally Ravi finishes off the remaining work in 13 days. In how many days Ravi alone could have alone done the work?Correct answer is '24'. Can you explain this answer?.
Rahul and Rajesh together can complete a piece of work in 12 days, which Rajesh and Ravi together can complete in 16 days. After Rahul has been working at it for 5 days, he leaves and Rajesh takes over for the next 7 days, before he leaves too, and finally Ravi finishes off the remaining work in 13 days. In how many days Ravi alone could have alone done the work?Correct answer is '24'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Rahul and Rajesh together can complete a piece of work in 12 days, which Rajesh and Ravi together can complete in 16 days. After Rahul has been working at it for 5 days, he leaves and Rajesh takes over for the next 7 days, before he leaves too, and finally Ravi finishes off the remaining work in 13 days. In how many days Ravi alone could have alone done the work?Correct answer is '24'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Rahul and Rajesh together can complete a piece of work in 12 days, which Rajesh and Ravi together can complete in 16 days. After Rahul has been working at it for 5 days, he leaves and Rajesh takes over for the next 7 days, before he leaves too, and finally Ravi finishes off the remaining work in 13 days. In how many days Ravi alone could have alone done the work?Correct answer is '24'. Can you explain this answer?.
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