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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?
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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.
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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.
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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?
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