CAT Exam > CAT Questions > Three friends A, B and C have decided to comp...
Start Learning for Free
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?
Most Upvoted Answer
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.
Community Answer
Three friends A, B and C have decided to complete a work together. The...
Stucked
Attention CAT Students!
To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CAT.
|
Explore Courses for CAT exam
|
|
Similar CAT Doubts
Top Courses for CATView all
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?
Question Description
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?.
Solutions 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? in English & in Hindi are available as part of our courses for CAT.
Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of
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?, a detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an
ample number of questions to practice 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? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup