CAT Exam > CAT Questions > DIRECTIONSfor the question:Solve the followin...
Start Learning for Free
DIRECTIONS for the question: Solve the following question and mark the best possible option.
A, B and C complete a particular work in 80 days when A and C worked on all 80 days, whereas B worked on every alternate day. A and B can together complete the work in 90 days and A and C in 120 days. In how many days would C alone take to complete the work?
- a)360 days
- b)90 days
- c)150 days
- d)180 days
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
DIRECTIONSfor the question:Solve the following question and mark the b...
►Let the units of work done by A, B and C in a single day be a, b and c respectively.
►We know that 90 (a + b) = 120 (a + c)
►Solving we get, a + 4c = 3b ---- (1)
►Also, 80 (a + c) + 40 b = 120 (a + c)
►So 40 (a + c) = 40 b
►Or a + c = b ----------- (2)
►So 40 (a + c) = 40 b
►Or a + c = b ----------- (2)
►Solving equation (1) and (2) together,
►we get
►we get
3b - 4c = b - c
=> 2b = 3c
=> b = 3/2 c
=> a = 1/2 c
=> 2b = 3c
=> b = 3/2 c
=> a = 1/2 c
►Now, total work done = 90 (a + b) = 90 (3c/2 + c/2 ) = 90 (2c) = 180 c
So, working alone C will take 180 c / c = 180 days
So, working alone C will take 180 c / c = 180 days
Most Upvoted Answer
DIRECTIONSfor the question:Solve the following question and mark the b...
To solve this question, we can use the concept of work done per day. Let's denote the work done by A, B, and C per day as x, y, and z respectively.
1. Working together:
Given that A and B can complete the work in 90 days, we can write the equation:
(A's work per day + B's work per day) x (number of days) = total work
(x + y) x 90 = 1
=> x + y = 1/90
2. A and C working together:
Given that A and C can complete the work in 120 days, we can write the equation:
(A's work per day + C's work per day) x (number of days) = total work
(x + z) x 120 = 1
=> x + z = 1/120
3. A, B, and C working together:
Given that A, B, and C complete the work in 80 days when A and C work on all 80 days and B works on every alternate day, we can write the equation:
(A's work per day + B's work per day + C's work per day) x (number of days) = total work
(x + y/2 + z) x 80 = 1
=> 2x + y + 2z = 1/80
=> 2x + 2z = 1/80 - y/80
=> 2(x + z) = 1/80 - y/80
=> x + z = 1/160 - y/160
=> x + z = (1 - y)/160
Comparing equations 2 and 3, we get:
1/120 = (1 - y)/160
=> 160 = 120(1 - y)
=> 160 = 120 - 120y
=> 40 = -120y
=> y = -1/3
Substituting the value of y in equation 1, we get:
x + (-1/3) = 1/90
=> x = 1/90 + 1/3
=> x = 11/90
Now, we can find the time taken by C alone to complete the work:
C's work per day = z = 1 - (x + y)
=> z = 1 - (11/90 + (-1/3))
=> z = 1 - (11/90 - 30/90)
=> z = 1 - (-19/90)
=> z = 1 + 19/90
=> z = 109/90
Therefore, C alone would take 90/109 days to complete the work, which is approximately 0.826 days. Rounding it off, C alone would take 1 day to complete the work.
Hence, the correct answer is option 'D' - 180 days.
1. Working together:
Given that A and B can complete the work in 90 days, we can write the equation:
(A's work per day + B's work per day) x (number of days) = total work
(x + y) x 90 = 1
=> x + y = 1/90
2. A and C working together:
Given that A and C can complete the work in 120 days, we can write the equation:
(A's work per day + C's work per day) x (number of days) = total work
(x + z) x 120 = 1
=> x + z = 1/120
3. A, B, and C working together:
Given that A, B, and C complete the work in 80 days when A and C work on all 80 days and B works on every alternate day, we can write the equation:
(A's work per day + B's work per day + C's work per day) x (number of days) = total work
(x + y/2 + z) x 80 = 1
=> 2x + y + 2z = 1/80
=> 2x + 2z = 1/80 - y/80
=> 2(x + z) = 1/80 - y/80
=> x + z = 1/160 - y/160
=> x + z = (1 - y)/160
Comparing equations 2 and 3, we get:
1/120 = (1 - y)/160
=> 160 = 120(1 - y)
=> 160 = 120 - 120y
=> 40 = -120y
=> y = -1/3
Substituting the value of y in equation 1, we get:
x + (-1/3) = 1/90
=> x = 1/90 + 1/3
=> x = 11/90
Now, we can find the time taken by C alone to complete the work:
C's work per day = z = 1 - (x + y)
=> z = 1 - (11/90 + (-1/3))
=> z = 1 - (11/90 - 30/90)
=> z = 1 - (-19/90)
=> z = 1 + 19/90
=> z = 109/90
Therefore, C alone would take 90/109 days to complete the work, which is approximately 0.826 days. Rounding it off, C alone would take 1 day to complete the work.
Hence, the correct answer is option 'D' - 180 days.
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
DIRECTIONSfor the question:Solve the following question and mark the best possible option.A, B and C complete a particular work in 80 days when A and C worked on all 80 days, whereas B worked on every alternate day. A and B can together complete the work in 90 days and A and C in 120 days. In how many days would C alone take to complete the work?a)360 daysb)90 daysc)150 daysd)180 daysCorrect answer is option 'D'. Can you explain this answer?
Question Description
DIRECTIONSfor the question:Solve the following question and mark the best possible option.A, B and C complete a particular work in 80 days when A and C worked on all 80 days, whereas B worked on every alternate day. A and B can together complete the work in 90 days and A and C in 120 days. In how many days would C alone take to complete the work?a)360 daysb)90 daysc)150 daysd)180 daysCorrect answer is option 'D'. 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 DIRECTIONSfor the question:Solve the following question and mark the best possible option.A, B and C complete a particular work in 80 days when A and C worked on all 80 days, whereas B worked on every alternate day. A and B can together complete the work in 90 days and A and C in 120 days. In how many days would C alone take to complete the work?a)360 daysb)90 daysc)150 daysd)180 daysCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for DIRECTIONSfor the question:Solve the following question and mark the best possible option.A, B and C complete a particular work in 80 days when A and C worked on all 80 days, whereas B worked on every alternate day. A and B can together complete the work in 90 days and A and C in 120 days. In how many days would C alone take to complete the work?a)360 daysb)90 daysc)150 daysd)180 daysCorrect answer is option 'D'. Can you explain this answer?.
DIRECTIONSfor the question:Solve the following question and mark the best possible option.A, B and C complete a particular work in 80 days when A and C worked on all 80 days, whereas B worked on every alternate day. A and B can together complete the work in 90 days and A and C in 120 days. In how many days would C alone take to complete the work?a)360 daysb)90 daysc)150 daysd)180 daysCorrect answer is option 'D'. 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 DIRECTIONSfor the question:Solve the following question and mark the best possible option.A, B and C complete a particular work in 80 days when A and C worked on all 80 days, whereas B worked on every alternate day. A and B can together complete the work in 90 days and A and C in 120 days. In how many days would C alone take to complete the work?a)360 daysb)90 daysc)150 daysd)180 daysCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for DIRECTIONSfor the question:Solve the following question and mark the best possible option.A, B and C complete a particular work in 80 days when A and C worked on all 80 days, whereas B worked on every alternate day. A and B can together complete the work in 90 days and A and C in 120 days. In how many days would C alone take to complete the work?a)360 daysb)90 daysc)150 daysd)180 daysCorrect answer is option 'D'. Can you explain this answer?.
Solutions for DIRECTIONSfor the question:Solve the following question and mark the best possible option.A, B and C complete a particular work in 80 days when A and C worked on all 80 days, whereas B worked on every alternate day. A and B can together complete the work in 90 days and A and C in 120 days. In how many days would C alone take to complete the work?a)360 daysb)90 daysc)150 daysd)180 daysCorrect answer is option 'D'. 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 DIRECTIONSfor the question:Solve the following question and mark the best possible option.A, B and C complete a particular work in 80 days when A and C worked on all 80 days, whereas B worked on every alternate day. A and B can together complete the work in 90 days and A and C in 120 days. In how many days would C alone take to complete the work?a)360 daysb)90 daysc)150 daysd)180 daysCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
DIRECTIONSfor the question:Solve the following question and mark the best possible option.A, B and C complete a particular work in 80 days when A and C worked on all 80 days, whereas B worked on every alternate day. A and B can together complete the work in 90 days and A and C in 120 days. In how many days would C alone take to complete the work?a)360 daysb)90 daysc)150 daysd)180 daysCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for DIRECTIONSfor the question:Solve the following question and mark the best possible option.A, B and C complete a particular work in 80 days when A and C worked on all 80 days, whereas B worked on every alternate day. A and B can together complete the work in 90 days and A and C in 120 days. In how many days would C alone take to complete the work?a)360 daysb)90 daysc)150 daysd)180 daysCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of DIRECTIONSfor the question:Solve the following question and mark the best possible option.A, B and C complete a particular work in 80 days when A and C worked on all 80 days, whereas B worked on every alternate day. A and B can together complete the work in 90 days and A and C in 120 days. In how many days would C alone take to complete the work?a)360 daysb)90 daysc)150 daysd)180 daysCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice DIRECTIONSfor the question:Solve the following question and mark the best possible option.A, B and C complete a particular work in 80 days when A and C worked on all 80 days, whereas B worked on every alternate day. A and B can together complete the work in 90 days and A and C in 120 days. In how many days would C alone take to complete the work?a)360 daysb)90 daysc)150 daysd)180 daysCorrect answer is option 'D'. 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
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup