CAT Exam > CAT Questions > Three people are working on a project. Toget...
Start Learning for Free
Three people are working on a project. Together, they take 10 hours to complete it. They start working together and after 5 hours, A left because he had completed his part (one-third) of the project. B also left along with A. C now takes 20 hours to finish the remaining part of the project. Find the time taken to complete the project of only B had been working on it.
- a)120 hrs
- b)40 hrs
- c)90 hrs
- d)15 hrs
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
Three people are working on a project. Together, they take 10 hours t...
Let's assume that the total work in the project is represented by 'W'.
First, let's find the work done by A, B, and C individually:
- A completes one-third of the project, so the work done by A is (1/3)W.
- After A leaves, B and C together complete the remaining two-thirds of the project in 5 hours. So, their combined work rate is (2/5)W per hour.
- C takes 20 hours to complete the remaining part of the project, which is one-third of the total work. So, the work done by C is (1/3)W.
Now, let's calculate the total work done by A, B, and C together:
Since A completes one-third of the project, the work done by A is (1/3)W.
After A leaves, B and C together complete the remaining two-thirds of the project in 5 hours. So, their combined work rate is (2/5)W per hour. Therefore, the work done by B and C together in 5 hours is (2/5)*(2/3)W = (4/15)W.
We know that A, B, and C together take 10 hours to complete the project.
So, the equation becomes:
(1/3)W + (4/15)W + (1/3)W = W
Simplifying the equation, we get:
5/15W + 4/15W + 5/15W = W
14/15W = W
Multiplying both sides by 15, we get:
14W = 15W
W = 14
Therefore, the total work in the project is 14 units.
Now, let's calculate the time taken to complete the project if only B had been working on it:
Since B alone completes two-thirds of the project in 5 hours, we can set up the equation as follows:
(2/3)*14 = (2/5)*B*t
Simplifying the equation, we get:
28 = (2/5)*B*t
Multiplying both sides by 5/2, we get:
B*t = 28*(5/2)
B*t = 70
Since B is working alone, the time taken to complete the project is 't' hours. Therefore, we can rewrite the equation as:
B = 70/t
So, the time taken to complete the project if only B had been working on it is equal to 70 divided by the rate of work of B, which is 't' hours.
Option A, 120 hours, is the correct answer.
First, let's find the work done by A, B, and C individually:
- A completes one-third of the project, so the work done by A is (1/3)W.
- After A leaves, B and C together complete the remaining two-thirds of the project in 5 hours. So, their combined work rate is (2/5)W per hour.
- C takes 20 hours to complete the remaining part of the project, which is one-third of the total work. So, the work done by C is (1/3)W.
Now, let's calculate the total work done by A, B, and C together:
Since A completes one-third of the project, the work done by A is (1/3)W.
After A leaves, B and C together complete the remaining two-thirds of the project in 5 hours. So, their combined work rate is (2/5)W per hour. Therefore, the work done by B and C together in 5 hours is (2/5)*(2/3)W = (4/15)W.
We know that A, B, and C together take 10 hours to complete the project.
So, the equation becomes:
(1/3)W + (4/15)W + (1/3)W = W
Simplifying the equation, we get:
5/15W + 4/15W + 5/15W = W
14/15W = W
Multiplying both sides by 15, we get:
14W = 15W
W = 14
Therefore, the total work in the project is 14 units.
Now, let's calculate the time taken to complete the project if only B had been working on it:
Since B alone completes two-thirds of the project in 5 hours, we can set up the equation as follows:
(2/3)*14 = (2/5)*B*t
Simplifying the equation, we get:
28 = (2/5)*B*t
Multiplying both sides by 5/2, we get:
B*t = 28*(5/2)
B*t = 70
Since B is working alone, the time taken to complete the project is 't' hours. Therefore, we can rewrite the equation as:
B = 70/t
So, the time taken to complete the project if only B had been working on it is equal to 70 divided by the rate of work of B, which is 't' hours.
Option A, 120 hours, is the correct answer.
Free Test
FREE
| Start Free Test |
Community Answer
Three people are working on a project. Together, they take 10 hours t...
Let the work per hour of A, B and C be a, b and c respectively.
Total work that needs to be done = 10(a+b+c). After 5 hours, work remaining = 5(a+b+c) which is done by c in 20 hours.
Therefore, 5(a+b+c) = 20c -> (1)
Since A completed one-third of the project by working for 5 hrs, we have 5a = (10/3)*(a+b+c) -> (2).
From (1) and (2), we get, a = 8b and c = 3b.
Therefore, total work involved in the project = 10*12b = 120b. Working alone, B takes 120 hours to finish it.
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 people are working on a project. Together, they take 10 hours to complete it. They start working together and after 5 hours, A left because he had completed his part (one-third) of the project. B also left along with A. C now takes 20 hours to finish the remaining part of the project. Find the time taken to complete the project of only B had been working on it.a)120 hrsb)40 hrsc)90 hrsd)15 hrsCorrect answer is option 'A'. Can you explain this answer?
Question Description
Three people are working on a project. Together, they take 10 hours to complete it. They start working together and after 5 hours, A left because he had completed his part (one-third) of the project. B also left along with A. C now takes 20 hours to finish the remaining part of the project. Find the time taken to complete the project of only B had been working on it.a)120 hrsb)40 hrsc)90 hrsd)15 hrsCorrect answer is option 'A'. 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 Three people are working on a project. Together, they take 10 hours to complete it. They start working together and after 5 hours, A left because he had completed his part (one-third) of the project. B also left along with A. C now takes 20 hours to finish the remaining part of the project. Find the time taken to complete the project of only B had been working on it.a)120 hrsb)40 hrsc)90 hrsd)15 hrsCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three people are working on a project. Together, they take 10 hours to complete it. They start working together and after 5 hours, A left because he had completed his part (one-third) of the project. B also left along with A. C now takes 20 hours to finish the remaining part of the project. Find the time taken to complete the project of only B had been working on it.a)120 hrsb)40 hrsc)90 hrsd)15 hrsCorrect answer is option 'A'. Can you explain this answer?.
Three people are working on a project. Together, they take 10 hours to complete it. They start working together and after 5 hours, A left because he had completed his part (one-third) of the project. B also left along with A. C now takes 20 hours to finish the remaining part of the project. Find the time taken to complete the project of only B had been working on it.a)120 hrsb)40 hrsc)90 hrsd)15 hrsCorrect answer is option 'A'. 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 Three people are working on a project. Together, they take 10 hours to complete it. They start working together and after 5 hours, A left because he had completed his part (one-third) of the project. B also left along with A. C now takes 20 hours to finish the remaining part of the project. Find the time taken to complete the project of only B had been working on it.a)120 hrsb)40 hrsc)90 hrsd)15 hrsCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three people are working on a project. Together, they take 10 hours to complete it. They start working together and after 5 hours, A left because he had completed his part (one-third) of the project. B also left along with A. C now takes 20 hours to finish the remaining part of the project. Find the time taken to complete the project of only B had been working on it.a)120 hrsb)40 hrsc)90 hrsd)15 hrsCorrect answer is option 'A'. Can you explain this answer?.
Solutions for Three people are working on a project. Together, they take 10 hours to complete it. They start working together and after 5 hours, A left because he had completed his part (one-third) of the project. B also left along with A. C now takes 20 hours to finish the remaining part of the project. Find the time taken to complete the project of only B had been working on it.a)120 hrsb)40 hrsc)90 hrsd)15 hrsCorrect answer is option 'A'. Can you explain this answer? 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 people are working on a project. Together, they take 10 hours to complete it. They start working together and after 5 hours, A left because he had completed his part (one-third) of the project. B also left along with A. C now takes 20 hours to finish the remaining part of the project. Find the time taken to complete the project of only B had been working on it.a)120 hrsb)40 hrsc)90 hrsd)15 hrsCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Three people are working on a project. Together, they take 10 hours to complete it. They start working together and after 5 hours, A left because he had completed his part (one-third) of the project. B also left along with A. C now takes 20 hours to finish the remaining part of the project. Find the time taken to complete the project of only B had been working on it.a)120 hrsb)40 hrsc)90 hrsd)15 hrsCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for Three people are working on a project. Together, they take 10 hours to complete it. They start working together and after 5 hours, A left because he had completed his part (one-third) of the project. B also left along with A. C now takes 20 hours to finish the remaining part of the project. Find the time taken to complete the project of only B had been working on it.a)120 hrsb)40 hrsc)90 hrsd)15 hrsCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of Three people are working on a project. Together, they take 10 hours to complete it. They start working together and after 5 hours, A left because he had completed his part (one-third) of the project. B also left along with A. C now takes 20 hours to finish the remaining part of the project. Find the time taken to complete the project of only B had been working on it.a)120 hrsb)40 hrsc)90 hrsd)15 hrsCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Three people are working on a project. Together, they take 10 hours to complete it. They start working together and after 5 hours, A left because he had completed his part (one-third) of the project. B also left along with A. C now takes 20 hours to finish the remaining part of the project. Find the time taken to complete the project of only B had been working on it.a)120 hrsb)40 hrsc)90 hrsd)15 hrsCorrect answer is option 'A'. Can you explain this answer? 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