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Three friends A, B and C have decided to complete a work together. The time taken by A, working alone, to the complete the work is 12.5% more than the time taken by B and C, working together, to complete the work. The time taken by B, working alone, is 426/7% more than the time taken by A and C, working together, to complete the work. If C, working alone, takes 63 days to complete the work, find the time taken by all three of them together to complete the work?
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Three friends A, B and C have decided to complete a work together. The...
Problem: Three friends A, B and C have decided to complete a work together. The time taken by A, working alone, to the complete the work is 12.5% more than the time taken by B and C, working together, to complete the work. The time taken by B, working alone, is 426/7% more than the time taken by A and C, working together, to complete the work. If C, working alone, takes 63 days to complete the work, find the time taken by all three of them together to complete the work?
Solution:
Let's assume that the time taken by A, B and C, working together, to complete the work is x days.
Then, as per the given information:
- The time taken by A, working alone, to complete the work is 12.5% more than x. So, the time taken by A, working alone, is (112.5/100)x days.
- The time taken by B, working alone, to complete the work is 426/7% more than x. So, the time taken by B, working alone, is (542/49)x days.
Now, let's find the work done by each person in a day:
- Work done by A in a day = 1/(112.5/100)x = (8/9)x
- Work done by B in a day = 1/(542/49)x = (49/542)x
- Work done by C in a day = 1/63
Therefore, the total work done by all three of them in a day = (8/9)x + (49/542)x + 1/63
Simplifying this expression, we get:
(4579x + 441)/4914
As per the given problem, all three of them are working together to complete the work. So, the time taken by all three of them together to complete the work is:
Total work/Work done by all three of them in a day
= 1/[(4579x + 441)/4914]
= 4914/(4579x + 441)
Now, we need to find the value of x to calculate the time taken by all three of them to complete the work.
As per the given problem, C takes 63 days to complete the work. So, we can say that:
1/63 = (8/9)x + (49/542)x + 1/63
Solving this equation, we get:
x = 77/46
Now, substituting the value of x in the expression we got earlier, we get:
Time taken by all three of them to complete the work = 4914/(4579*(77/46) + 441)
= 31 days (approx.)
Hence, all three of them will take 31 days to complete the work together.
Solution:
Let's assume that the time taken by A, B and C, working together, to complete the work is x days.
Then, as per the given information:
- The time taken by A, working alone, to complete the work is 12.5% more than x. So, the time taken by A, working alone, is (112.5/100)x days.
- The time taken by B, working alone, to complete the work is 426/7% more than x. So, the time taken by B, working alone, is (542/49)x days.
Now, let's find the work done by each person in a day:
- Work done by A in a day = 1/(112.5/100)x = (8/9)x
- Work done by B in a day = 1/(542/49)x = (49/542)x
- Work done by C in a day = 1/63
Therefore, the total work done by all three of them in a day = (8/9)x + (49/542)x + 1/63
Simplifying this expression, we get:
(4579x + 441)/4914
As per the given problem, all three of them are working together to complete the work. So, the time taken by all three of them together to complete the work is:
Total work/Work done by all three of them in a day
= 1/[(4579x + 441)/4914]
= 4914/(4579x + 441)
Now, we need to find the value of x to calculate the time taken by all three of them to complete the work.
As per the given problem, C takes 63 days to complete the work. So, we can say that:
1/63 = (8/9)x + (49/542)x + 1/63
Solving this equation, we get:
x = 77/46
Now, substituting the value of x in the expression we got earlier, we get:
Time taken by all three of them to complete the work = 4914/(4579*(77/46) + 441)
= 31 days (approx.)
Hence, all three of them will take 31 days to complete the work together.
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Three friends A, B and C have decided to complete a work together. The time taken by A, working alone, to the complete the work is 12.5% more than the time taken by B and C, working together, to complete the work. The time taken by B, working alone, is 426/7% more than the time taken by A and C, working together, to complete the work. If C, working alone, takes 63 days to complete the work, find the time taken by all three of them together to complete the work?
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Three friends A, B and C have decided to complete a work together. The time taken by A, working alone, to the complete the work is 12.5% more than the time taken by B and C, working together, to complete the work. The time taken by B, working alone, is 426/7% more than the time taken by A and C, working together, to complete the work. If C, working alone, takes 63 days to complete the work, find the time taken by all three of them together to 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 Three friends A, B and C have decided to complete a work together. The time taken by A, working alone, to the complete the work is 12.5% more than the time taken by B and C, working together, to complete the work. The time taken by B, working alone, is 426/7% more than the time taken by A and C, working together, to complete the work. If C, working alone, takes 63 days to complete the work, find the time taken by all three of them together to complete the work? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three friends A, B and C have decided to complete a work together. The time taken by A, working alone, to the complete the work is 12.5% more than the time taken by B and C, working together, to complete the work. The time taken by B, working alone, is 426/7% more than the time taken by A and C, working together, to complete the work. If C, working alone, takes 63 days to complete the work, find the time taken by all three of them together to complete the work?.
Three friends A, B and C have decided to complete a work together. The time taken by A, working alone, to the complete the work is 12.5% more than the time taken by B and C, working together, to complete the work. The time taken by B, working alone, is 426/7% more than the time taken by A and C, working together, to complete the work. If C, working alone, takes 63 days to complete the work, find the time taken by all three of them together to 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 Three friends A, B and C have decided to complete a work together. The time taken by A, working alone, to the complete the work is 12.5% more than the time taken by B and C, working together, to complete the work. The time taken by B, working alone, is 426/7% more than the time taken by A and C, working together, to complete the work. If C, working alone, takes 63 days to complete the work, find the time taken by all three of them together to complete the work? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three friends A, B and C have decided to complete a work together. The time taken by A, working alone, to the complete the work is 12.5% more than the time taken by B and C, working together, to complete the work. The time taken by B, working alone, is 426/7% more than the time taken by A and C, working together, to complete the work. If C, working alone, takes 63 days to complete the work, find the time taken by all three of them together to complete the work?.
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