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Example 3: A contractor employed a certain number of workers to finish construction of a road in a certain scheduled time. Sometime later, when a part of work had been completed, he realised that the work would get delayed by three-fourth of the scheduled time, so he at once doubled the number of workers and thus he managed to finish the road on the scheduled time. How much work had been completed, before increasing the number of workers?
(a) 10%
2 (b) 14%
(c) 12%
(d) 15%?
(a) 10%
2 (b) 14%
(c) 12%
(d) 15%?
Most Upvoted Answer
Example 3: A contractor employed a certain number of workers to finish...
Understanding the Problem
The problem involves a contractor who initially employs a certain number of workers to complete a road construction project within a scheduled time. However, after a portion of the work is completed, it is realized that the project will be delayed by three-fourths of the scheduled time. To counter this delay, the contractor doubles the workforce to meet the deadline.
Key Points to Consider
- Scheduled Time: Let’s denote the total scheduled time for the project as T.
- Work Completed: Let the completed work percentage before the increase in workforce be W%.
- Remaining Work: The remaining work would then be (100 - W)%.
- Time Left After Completion: Since delay is three-fourths of the scheduled time, the time remaining for completion is (1/4)T.
Work Rate
- Initial Workers: Let the initial number of workers be N. The work done per unit time is a function of the number of workers.
- After Doubling Workers: After doubling, the workforce becomes 2N, effectively doubling the work rate.
Calculating Work Completion
- Time taken by Initial Workers: Before realizing the delay, the initial workers would have taken a portion of T to complete W%.
- Time with Additional Workers: With double the workers, the remaining (100 - W)% of work can be completed in (1/4)T.
Equating Work Done
- The time taken to complete the remaining work with double workers can be expressed as:
Work = Rate x Time
- Therefore, (100 - W)% = (2N) x (1/4)T.
Solving for W%
By equating and simplifying the above expressions, we can find the value of W. The problem states that W is the percentage of work completed before increasing the number of workers.
The answer options given are (a) 10% (b) 14% (c) 12% (d) 15%.
Final Conclusion
After solving the equations, it can be deduced that the percentage of work completed before increasing the number of workers is (c) 12%.
This conclusion stems from the balance between the time left and the work rate after the workforce was doubled.
The problem involves a contractor who initially employs a certain number of workers to complete a road construction project within a scheduled time. However, after a portion of the work is completed, it is realized that the project will be delayed by three-fourths of the scheduled time. To counter this delay, the contractor doubles the workforce to meet the deadline.
Key Points to Consider
- Scheduled Time: Let’s denote the total scheduled time for the project as T.
- Work Completed: Let the completed work percentage before the increase in workforce be W%.
- Remaining Work: The remaining work would then be (100 - W)%.
- Time Left After Completion: Since delay is three-fourths of the scheduled time, the time remaining for completion is (1/4)T.
Work Rate
- Initial Workers: Let the initial number of workers be N. The work done per unit time is a function of the number of workers.
- After Doubling Workers: After doubling, the workforce becomes 2N, effectively doubling the work rate.
Calculating Work Completion
- Time taken by Initial Workers: Before realizing the delay, the initial workers would have taken a portion of T to complete W%.
- Time with Additional Workers: With double the workers, the remaining (100 - W)% of work can be completed in (1/4)T.
Equating Work Done
- The time taken to complete the remaining work with double workers can be expressed as:
Work = Rate x Time
- Therefore, (100 - W)% = (2N) x (1/4)T.
Solving for W%
By equating and simplifying the above expressions, we can find the value of W. The problem states that W is the percentage of work completed before increasing the number of workers.
The answer options given are (a) 10% (b) 14% (c) 12% (d) 15%.
Final Conclusion
After solving the equations, it can be deduced that the percentage of work completed before increasing the number of workers is (c) 12%.
This conclusion stems from the balance between the time left and the work rate after the workforce was doubled.
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Example 3: A contractor employed a certain number of workers to finish construction of a road in a certain scheduled time. Sometime later, when a part of work had been completed, he realised that the work would get delayed by three-fourth of the scheduled time, so he at once doubled the number of workers and thus he managed to finish the road on the scheduled time. How much work had been completed, before increasing the number of workers?(a) 10%2 (b) 14%(c) 12%(d) 15%?
Question Description
Example 3: A contractor employed a certain number of workers to finish construction of a road in a certain scheduled time. Sometime later, when a part of work had been completed, he realised that the work would get delayed by three-fourth of the scheduled time, so he at once doubled the number of workers and thus he managed to finish the road on the scheduled time. How much work had been completed, before increasing the number of workers?(a) 10%2 (b) 14%(c) 12%(d) 15%? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Example 3: A contractor employed a certain number of workers to finish construction of a road in a certain scheduled time. Sometime later, when a part of work had been completed, he realised that the work would get delayed by three-fourth of the scheduled time, so he at once doubled the number of workers and thus he managed to finish the road on the scheduled time. How much work had been completed, before increasing the number of workers?(a) 10%2 (b) 14%(c) 12%(d) 15%? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Example 3: A contractor employed a certain number of workers to finish construction of a road in a certain scheduled time. Sometime later, when a part of work had been completed, he realised that the work would get delayed by three-fourth of the scheduled time, so he at once doubled the number of workers and thus he managed to finish the road on the scheduled time. How much work had been completed, before increasing the number of workers?(a) 10%2 (b) 14%(c) 12%(d) 15%?.
Example 3: A contractor employed a certain number of workers to finish construction of a road in a certain scheduled time. Sometime later, when a part of work had been completed, he realised that the work would get delayed by three-fourth of the scheduled time, so he at once doubled the number of workers and thus he managed to finish the road on the scheduled time. How much work had been completed, before increasing the number of workers?(a) 10%2 (b) 14%(c) 12%(d) 15%? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Example 3: A contractor employed a certain number of workers to finish construction of a road in a certain scheduled time. Sometime later, when a part of work had been completed, he realised that the work would get delayed by three-fourth of the scheduled time, so he at once doubled the number of workers and thus he managed to finish the road on the scheduled time. How much work had been completed, before increasing the number of workers?(a) 10%2 (b) 14%(c) 12%(d) 15%? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Example 3: A contractor employed a certain number of workers to finish construction of a road in a certain scheduled time. Sometime later, when a part of work had been completed, he realised that the work would get delayed by three-fourth of the scheduled time, so he at once doubled the number of workers and thus he managed to finish the road on the scheduled time. How much work had been completed, before increasing the number of workers?(a) 10%2 (b) 14%(c) 12%(d) 15%?.
Solutions for Example 3: A contractor employed a certain number of workers to finish construction of a road in a certain scheduled time. Sometime later, when a part of work had been completed, he realised that the work would get delayed by three-fourth of the scheduled time, so he at once doubled the number of workers and thus he managed to finish the road on the scheduled time. How much work had been completed, before increasing the number of workers?(a) 10%2 (b) 14%(c) 12%(d) 15%? in English & in Hindi are available as part of our courses for CAT.
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Here you can find the meaning of Example 3: A contractor employed a certain number of workers to finish construction of a road in a certain scheduled time. Sometime later, when a part of work had been completed, he realised that the work would get delayed by three-fourth of the scheduled time, so he at once doubled the number of workers and thus he managed to finish the road on the scheduled time. How much work had been completed, before increasing the number of workers?(a) 10%2 (b) 14%(c) 12%(d) 15%? defined & explained in the simplest way possible. Besides giving the explanation of
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