time n work problem

sohailmbaprep wrote:If 6 men can do a piece of work in 30 days of 9 hours each, how many men will it take to do 10 times the amount of work if they work for 25 days of 8 hours?

6 men do the work in 30*9 = 270 hours

25 days of 8 hours = 25*8 hours = 200 hours

To complete ten times of the work in 200 hours number of men required = 6*270*10/200 = 3*27 = 81

sohailmbaprep wrote:If 6 men can do a piece of work in 30 days of 9 hours each, how many men will it take to do 10
times the amount of work if they work for 25 days of 8 hours?

The hourly rate of the 6 men is 1/(30 x 9) = 1/270. If we let x = the number of men needed to do 10 times the work when they work for 25 days of 8 hours, then the hourly rate of these x men must be 10/(25 x 8) = 10/200 = 1/20. We can create the following proportion and solve for x:

6/(1/270) = x/(1/20)

1620 = 20x

x = [spoiler]1620/20 = 81[/spoiler]

Hi All,

While this is an older question, this type of 'work' prompt still sometimes appears on the Official GMAT (although it is rare). In these situations, it can often help to determine the total amount of 'work' needed to complete a task.

We're told that 6 men can do a piece of work in 30 days of 9 hours each. We're asked for the number of men needed to do 10 times the amount of work if they work for 25 days of 8 hours.

(6 men)(30 days each)(9 hours/day) = 1620 man-hours of work to complete the job

(X men)(25 days each)(8 hours/day) = 200X man-hours of work each day

For 10 TIMES the initial amount of work, we have...
200X = 16,200 man-hours of work
X = 81 men

Final Answer: 81

GMAT assassins aren't born, they're made,
Rich

sohailmbaprep wrote:If 6 men can do a piece of work in 30 days of 9 hours each, how many men will it take to do 10
times the amount of work if they work for 25 days of 8 hours?

The hourly rate of 6 men is 1/(30 x 9) = 1/270, and hence the hourly rate of 1 man is (1/270)/6 = 1/1620. The hourly rate to do 10 times the amount of work for 25 days of 8 hours is 10/(25 x 8) = 10/200 = 1/20. Since one man’s hourly rate is 1/1620, we need (1/20)/(1/1620) = 1/20 x 1620 = 81 men.

Alternate Solution:

The job done by 6 men in 30 days at 9 hours per day takes 30 x 9 = 270 hours. 10 times the amount of work will take 6 men 270 x 10 = 2700 hours. To do this job in 25 x 8 = 200 hours, in other words, to decrease the time by a factor of 2700/200 = 13.5, we need to increase the number of men by a factor of 13.5. Thus, we need 6 x 13.5 = 81 men.

Answer: 81