NandishSS wrote:40 employees take 30 days, working at 8 hrs per day, to complete a task. 40 employees start the work but after 10 days,20 leave and are replaced by employees who are 1/2 as productive.How many hours per day should the new team work if the work has to be completed in the scheduled timeline?
1. 12
2. 20
3. 10.6
4. 6
5. 30
The rate for the 40 workers is 1/(30 x 8) = 1/240 task/hour
So after 10 days, the amount of work completed is 1/240 x 10 x 8 = 80/240 = 1/3 of the job and thus 2/3 is left to be completed.
Since 20 workers leave, the rate of the remaining 20 workers is 1/2 x 1/240 = 1/480 task/hour and the 20 new workers who join in have a rate that is half of 1/480, or 1/960, task/hour. Thus the new rate of the 40 workers (20 original and 20 new workers) is 1/480 + 1/960 = 3/960 = 1/320 task/hour.
They still have to finish the task in 20 more days. If we let n = the number of hours they work per day, then it must be true that:
1/320 x 20 x n = 2/3
1/16 x n = 2/3
n = 2/3 x 16
n = 32/3 = 10 2/3 ≈ 10.6
Alternate Solution:
The number of worker-hours required for the entire job is 40 workers x 30 days x 8 hours/day = 9600 worker-hours. In the first 10 days, the workers have accomplished 40 workers x 10 days x 8 hours/day = 3200 worker-hours, leaving 6400 worker-hours to be accomplished.
The remaining work will be accomplished by 20 original workers plus 20 new workers who work at half-speed. The total amount of work accomplished, then, is equivalent to the work of 30 original workers.
With 6400 worker-hours needing to be done by (the equivalent of) 30 workers, we see that each worker will have to work for 6400/30 ≈ 213.33 hours. This needs to be done in 20 days, so each worker will have to work 213.33/20 ≈ 10.6 hours per day.
Answer:
C
