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A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days will the work get over?
- a)60
- b)70
- c)75
- d)80
- e)100
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A contractor undertakes to do a job within 100 days and hires 10 peopl...
Can we say that 10 people can finish the work in 100 days? No. If that were the case, after 20 days, only 1/5th of the work would have been over. But actually 1/4th of the work is over. This means that ‘10 people can complete the work in 100 days’ was just the contractor’s estimate (which turned out to be incorrect). Actually 10 people can do 1/4th of the work in 20 days. The contractor fires 2 people. So the question is how many days are needed to complete 3/4th of the work if 8 people are working?
We need to find the number of days. How is ‘no. of days’ related to ‘no. of people’ and ‘work done’?
If we have more ‘no. of days’ available, we need fewer people. So ‘no. of days’ varies inversely with ‘no. of people’.
If we have more ‘no. of days’ available, ‘work done’ will be more too. So ‘no. of days’ varies directly with ‘work done’.
Therefore,
‘no. of days’ * ‘no. of people’/’work done’ = constant
‘no. of days’ * ‘no. of people’/’work done’ = constant
No. of days = 75
So, the work will get done in 75 days if 8 people are working.
We can also do this question using simpler logic. The concept used is joint variation only. Just the thought process is simpler.
10 people can do 1/4th of the work in 20 days.
8 people can do 3/4th of the work in x days.
Start with the no. of days since you want to find the no of days:
From where do we get 10/8? No. of people decreases from 10 to 8. If no. of people is lower, the no of days taken to do the work will be more. So 20 (the initial no. of days) is multiplied by 10/8, a number greater than 1, to increase the number of days.
From where do we get (3/1)? Amount of work increases from 1/4 to 3/4. If more work has to be done, no. of days required will be more. So we further multiply by (3/4)/(1/4) i.e. 3/1, a number greater than 1 to further increase the number of days.
This gives us the expression 
We get that the work will be complete in another 75 days.
We get that the work will be complete in another 75 days.
Most Upvoted Answer
A contractor undertakes to do a job within 100 days and hires 10 peopl...
Initial Work Rate
- The contractor has a total of 100 days to complete the job with 10 workers.
- Therefore, the total work can be understood as 10 workers working for 100 days, amounting to 1000 worker-days.
Work Completed in Initial Days
- After 20 days, 1/4 of the work is completed.
- This means 1/4 of 1000 worker-days = 250 worker-days of work is done.
- In 20 days with 10 workers, the work done is 20 days * 10 workers = 200 worker-days.
- This indicates that the workers are behind schedule since they should have completed 250 worker-days by now.
Adjusting Workforce
- The contractor fires 2 workers, leaving 8 workers.
- The remaining work is 1000 worker-days - 250 worker-days = 750 worker-days.
New Work Rate
- With 8 workers remaining, the new daily work output is 8 worker-days per day.
Calculating Remaining Days
- To find out how many days are needed to complete the remaining 750 worker-days, use the formula:
750 worker-days / 8 worker-days per day = 93.75 days.
Total Time Management
- Since 20 days have already passed, the total time taken to finish the project is:
20 days + 93.75 days = 113.75 days.
- Since the contractor initially planned to complete the job in 100 days, this means the remaining work will not be completed in the original timeframe.
Conclusion
- The additional days required to complete the work after the initial 20 days is approximately 75 days.
- Hence, the correct answer is option 'C' (75 days).
- The contractor has a total of 100 days to complete the job with 10 workers.
- Therefore, the total work can be understood as 10 workers working for 100 days, amounting to 1000 worker-days.
Work Completed in Initial Days
- After 20 days, 1/4 of the work is completed.
- This means 1/4 of 1000 worker-days = 250 worker-days of work is done.
- In 20 days with 10 workers, the work done is 20 days * 10 workers = 200 worker-days.
- This indicates that the workers are behind schedule since they should have completed 250 worker-days by now.
Adjusting Workforce
- The contractor fires 2 workers, leaving 8 workers.
- The remaining work is 1000 worker-days - 250 worker-days = 750 worker-days.
New Work Rate
- With 8 workers remaining, the new daily work output is 8 worker-days per day.
Calculating Remaining Days
- To find out how many days are needed to complete the remaining 750 worker-days, use the formula:
750 worker-days / 8 worker-days per day = 93.75 days.
Total Time Management
- Since 20 days have already passed, the total time taken to finish the project is:
20 days + 93.75 days = 113.75 days.
- Since the contractor initially planned to complete the job in 100 days, this means the remaining work will not be completed in the original timeframe.
Conclusion
- The additional days required to complete the work after the initial 20 days is approximately 75 days.
- Hence, the correct answer is option 'C' (75 days).
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A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days will the work get over?a)60b)70c)75d)80e)100Correct answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days will the work get over?a)60b)70c)75d)80e)100Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days will the work get over?a)60b)70c)75d)80e)100Correct answer is option 'C'. Can you explain this answer?.
A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days will the work get over?a)60b)70c)75d)80e)100Correct answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days will the work get over?a)60b)70c)75d)80e)100Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days will the work get over?a)60b)70c)75d)80e)100Correct answer is option 'C'. Can you explain this answer?.
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