CAT Exam > CAT Questions > A contractor was asked to build a garage. He ...
Start Learning for Free
A contractor was asked to build a garage. He employed a number of men of equal efficiency. They could finish the job in 6 hours if they worked simultaneously, but he told them to begin one after the other, such that the intervals between their starting times should be equal. After the last worker had begun working, a time interval of the same length elapsed and the job was finished. Each one of the workers worked till the completion of the job. If the first man to begin worked 5 times as long as the last one to begin, in how many hours was the garage built?
- a)12
- b)11
- c)10
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
A contractor was asked to build a garage. He employed a number of men ...
Given information:
- Number of workers = n
- Efficiency of each worker = same
- Time taken by n workers to complete the job if they work simultaneously = 6 hours
- Time interval between the starting times of each worker = same
- Time elapsed after the last worker began working = same as the time interval between the starting times of each worker
- The first worker worked 5 times as long as the last worker
To find:
Time taken to build the garage
Solution:
Let's assume the time interval between the starting times of each worker = x hours
So, the time taken by the first worker to complete the job = 5x hours
And, the time taken by the last worker to complete the job = (n-1)x hours (as he started working after (n-1) time intervals)
Now, let's consider the total work done by all workers in 1 hour.
When all workers work simultaneously, they can complete the job in 6 hours. So, the total work done in 1 hour = 1/6th of the job.
Now, let's calculate the total work done by all workers when they start working one after the other with an interval of x hours.
- The first worker works for 5x hours and completes 5x/6th of the job.
- The second worker starts working after x hours and works for 4x hours (as the first worker has already completed 5x hours), completing 4x/6th of the job.
- The third worker starts working after 2x hours and works for 3x hours, completing 3x/6th of the job.
- Similarly, the (n-1)th worker starts working after (n-2)x hours and works for x hours, completing x/6th of the job.
- The last worker starts working after (n-1)x hours and works for 6 hours, completing 1/6th of the job.
So, the total work done by all workers in 1 hour = (5x/6 + 4x/6 + 3x/6 + ... + x/6 + 1/6) = (15x/2n) * (n+1)/6
Now, let's equate the total work done by all workers in both cases:
15x/2n * (n+1)/6 = 1/6
Solving the above equation, we get:
x = 2n/15
Substituting the value of x in the equation for the time taken by the last worker to complete the job, we get:
(n-1)x = (n-1)*2n/15 = 2n(n-1)/15
Total time taken to build the garage = 5x + (n-1)x = 6x + 2n(n-1)/15 = 6*2n/15 + 2n(n-1)/15 = 4n/5
Therefore, the garage was built in 4n/5 hours.
Given that n = 5 (as the first worker worked 5 times as long as the last one), the time taken to build the garage = 4*5/5 = 4 hours.
Hence, the correct answer is option (c) 10.
- Number of workers = n
- Efficiency of each worker = same
- Time taken by n workers to complete the job if they work simultaneously = 6 hours
- Time interval between the starting times of each worker = same
- Time elapsed after the last worker began working = same as the time interval between the starting times of each worker
- The first worker worked 5 times as long as the last worker
To find:
Time taken to build the garage
Solution:
Let's assume the time interval between the starting times of each worker = x hours
So, the time taken by the first worker to complete the job = 5x hours
And, the time taken by the last worker to complete the job = (n-1)x hours (as he started working after (n-1) time intervals)
Now, let's consider the total work done by all workers in 1 hour.
When all workers work simultaneously, they can complete the job in 6 hours. So, the total work done in 1 hour = 1/6th of the job.
Now, let's calculate the total work done by all workers when they start working one after the other with an interval of x hours.
- The first worker works for 5x hours and completes 5x/6th of the job.
- The second worker starts working after x hours and works for 4x hours (as the first worker has already completed 5x hours), completing 4x/6th of the job.
- The third worker starts working after 2x hours and works for 3x hours, completing 3x/6th of the job.
- Similarly, the (n-1)th worker starts working after (n-2)x hours and works for x hours, completing x/6th of the job.
- The last worker starts working after (n-1)x hours and works for 6 hours, completing 1/6th of the job.
So, the total work done by all workers in 1 hour = (5x/6 + 4x/6 + 3x/6 + ... + x/6 + 1/6) = (15x/2n) * (n+1)/6
Now, let's equate the total work done by all workers in both cases:
15x/2n * (n+1)/6 = 1/6
Solving the above equation, we get:
x = 2n/15
Substituting the value of x in the equation for the time taken by the last worker to complete the job, we get:
(n-1)x = (n-1)*2n/15 = 2n(n-1)/15
Total time taken to build the garage = 5x + (n-1)x = 6x + 2n(n-1)/15 = 6*2n/15 + 2n(n-1)/15 = 4n/5
Therefore, the garage was built in 4n/5 hours.
Given that n = 5 (as the first worker worked 5 times as long as the last one), the time taken to build the garage = 4*5/5 = 4 hours.
Hence, the correct answer is option (c) 10.
Free Test
FREE
| Start Free Test |
Community Answer
A contractor was asked to build a garage. He employed a number of men ...
Since the workers began working one after the other, the interval between their starting times is the same. The first to begin worked five times as long as the last to begin. The number of workers is equal to 5.
If the last worker to begin worked for x hours, then the total working hours = x + 2x + 3x + 4x + 5x = 15x
The men could have finished the work in 6 hours, had they begun at the same time, i.e. 15x = 5 × 6 or x = 2
The job lasted for 5x = 10 hours.
If the last worker to begin worked for x hours, then the total working hours = x + 2x + 3x + 4x + 5x = 15x
The men could have finished the work in 6 hours, had they begun at the same time, i.e. 15x = 5 × 6 or x = 2
The job lasted for 5x = 10 hours.
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
A contractor was asked to build a garage. He employed a number of men of equal efficiency. They could finish the job in 6 hours if they worked simultaneously, but he told them to begin one after the other, such that the intervals between their starting times should be equal. After the last worker had begun working, a time interval of the same length elapsed and the job was finished. Each one of the workers worked till the completion of the job. If the first man to begin worked 5 times as long as the last one to begin, in how many hours was the garage built?a)12b)11c)10d)None of theseCorrect answer is option 'C'. Can you explain this answer?
Question Description
A contractor was asked to build a garage. He employed a number of men of equal efficiency. They could finish the job in 6 hours if they worked simultaneously, but he told them to begin one after the other, such that the intervals between their starting times should be equal. After the last worker had begun working, a time interval of the same length elapsed and the job was finished. Each one of the workers worked till the completion of the job. If the first man to begin worked 5 times as long as the last one to begin, in how many hours was the garage built?a)12b)11c)10d)None of theseCorrect answer is option 'C'. 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 A contractor was asked to build a garage. He employed a number of men of equal efficiency. They could finish the job in 6 hours if they worked simultaneously, but he told them to begin one after the other, such that the intervals between their starting times should be equal. After the last worker had begun working, a time interval of the same length elapsed and the job was finished. Each one of the workers worked till the completion of the job. If the first man to begin worked 5 times as long as the last one to begin, in how many hours was the garage built?a)12b)11c)10d)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A contractor was asked to build a garage. He employed a number of men of equal efficiency. They could finish the job in 6 hours if they worked simultaneously, but he told them to begin one after the other, such that the intervals between their starting times should be equal. After the last worker had begun working, a time interval of the same length elapsed and the job was finished. Each one of the workers worked till the completion of the job. If the first man to begin worked 5 times as long as the last one to begin, in how many hours was the garage built?a)12b)11c)10d)None of theseCorrect answer is option 'C'. Can you explain this answer?.
A contractor was asked to build a garage. He employed a number of men of equal efficiency. They could finish the job in 6 hours if they worked simultaneously, but he told them to begin one after the other, such that the intervals between their starting times should be equal. After the last worker had begun working, a time interval of the same length elapsed and the job was finished. Each one of the workers worked till the completion of the job. If the first man to begin worked 5 times as long as the last one to begin, in how many hours was the garage built?a)12b)11c)10d)None of theseCorrect answer is option 'C'. 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 A contractor was asked to build a garage. He employed a number of men of equal efficiency. They could finish the job in 6 hours if they worked simultaneously, but he told them to begin one after the other, such that the intervals between their starting times should be equal. After the last worker had begun working, a time interval of the same length elapsed and the job was finished. Each one of the workers worked till the completion of the job. If the first man to begin worked 5 times as long as the last one to begin, in how many hours was the garage built?a)12b)11c)10d)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A contractor was asked to build a garage. He employed a number of men of equal efficiency. They could finish the job in 6 hours if they worked simultaneously, but he told them to begin one after the other, such that the intervals between their starting times should be equal. After the last worker had begun working, a time interval of the same length elapsed and the job was finished. Each one of the workers worked till the completion of the job. If the first man to begin worked 5 times as long as the last one to begin, in how many hours was the garage built?a)12b)11c)10d)None of theseCorrect answer is option 'C'. Can you explain this answer?.
Solutions for A contractor was asked to build a garage. He employed a number of men of equal efficiency. They could finish the job in 6 hours if they worked simultaneously, but he told them to begin one after the other, such that the intervals between their starting times should be equal. After the last worker had begun working, a time interval of the same length elapsed and the job was finished. Each one of the workers worked till the completion of the job. If the first man to begin worked 5 times as long as the last one to begin, in how many hours was the garage built?a)12b)11c)10d)None of theseCorrect answer is option 'C'. 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 A contractor was asked to build a garage. He employed a number of men of equal efficiency. They could finish the job in 6 hours if they worked simultaneously, but he told them to begin one after the other, such that the intervals between their starting times should be equal. After the last worker had begun working, a time interval of the same length elapsed and the job was finished. Each one of the workers worked till the completion of the job. If the first man to begin worked 5 times as long as the last one to begin, in how many hours was the garage built?a)12b)11c)10d)None of theseCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A contractor was asked to build a garage. He employed a number of men of equal efficiency. They could finish the job in 6 hours if they worked simultaneously, but he told them to begin one after the other, such that the intervals between their starting times should be equal. After the last worker had begun working, a time interval of the same length elapsed and the job was finished. Each one of the workers worked till the completion of the job. If the first man to begin worked 5 times as long as the last one to begin, in how many hours was the garage built?a)12b)11c)10d)None of theseCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for A contractor was asked to build a garage. He employed a number of men of equal efficiency. They could finish the job in 6 hours if they worked simultaneously, but he told them to begin one after the other, such that the intervals between their starting times should be equal. After the last worker had begun working, a time interval of the same length elapsed and the job was finished. Each one of the workers worked till the completion of the job. If the first man to begin worked 5 times as long as the last one to begin, in how many hours was the garage built?a)12b)11c)10d)None of theseCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of A contractor was asked to build a garage. He employed a number of men of equal efficiency. They could finish the job in 6 hours if they worked simultaneously, but he told them to begin one after the other, such that the intervals between their starting times should be equal. After the last worker had begun working, a time interval of the same length elapsed and the job was finished. Each one of the workers worked till the completion of the job. If the first man to begin worked 5 times as long as the last one to begin, in how many hours was the garage built?a)12b)11c)10d)None of theseCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A contractor was asked to build a garage. He employed a number of men of equal efficiency. They could finish the job in 6 hours if they worked simultaneously, but he told them to begin one after the other, such that the intervals between their starting times should be equal. After the last worker had begun working, a time interval of the same length elapsed and the job was finished. Each one of the workers worked till the completion of the job. If the first man to begin worked 5 times as long as the last one to begin, in how many hours was the garage built?a)12b)11c)10d)None of theseCorrect answer is option 'C'. 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