40 employees take 30 days, working

[NandishSS]

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

Source: Experts' Global

OA: C

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Hi NandishSS,

We're told that 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 workers leave and are replaced by employees who are 1/2 as productive. We're asked for the number hours per day that the new team must work to complete the job in the scheduled timeline. With these types of rate questions, it helps to first figure out the total amount of 'work' needed to complete the job, then use that information with whatever other information you've been given.

The original team would need (40)(30)(8) = 9600 worker-hours to complete the job

For the first 10 days, all 40 employees work as planned, so (40)(10)(8) = 3200 worker-hours are completed, leaving 9600 - 3200 = 6400 worker-hours to go

20 of the 40 employees are replaced with workers who are HALF as productive, meaning that each of those employees completes 1/2 a worker-hour of work per 1 hour. With those 20 replacement workers, the 'new' team of 40 employees will complete LESS work per hour than the original team did.

New team:
20 original workers complete 20 worker-hours per hour
20 new workers complete 10 worker-hours per hour
20 + 10 = 30 worker-hours completed per hour

With 20 days remaining and 6400 worker-hours to go...
6400/20 = 320 worker-hours must be completed each day.

At the new rate, that would require...
320/30 = 10 2/3 hours of work per worker each day

Final Answer: C

GMAT assassins aren't born, they're made,
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[Jeff@TargetTestPrep]

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

[GMATGuruNY]

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

Let the rate for each of the 40 employees = 2 widgets per hour, implying the following:
Hourly rate for 40 employees = 2*40 = 80 widgets
Work produced over each 8-hour day = 8*80 = 640 widgets
Total amount of work to be produced for the 30-day job = 30*640 = 19200 widgets

Since the daily rate for 40 workers = 640 widgets, the work produced over the first 10 days = 10*640 = 6400 widgets.
Remaining work = 19200 - 6400 = 12800 widgets

Since the 20 replacement workers are half as productive as the 20 original employees, the resulting rate for the new team = 20*1 + 20*2 = 60 widgets per hour.
To complete 12800 widgets in the remaining 20 days, the daily work required = 12800/20 = 640 widgets.
For 640 widgets to be produced each day at a rate of 60 widgets per hour, the number of hours required = 640/60 ≈ 10.6

The correct answer is C.