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Time and work problem

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Time and work problem

by apex231 » Sat Jul 02, 2011 6:14 pm
A wall has to be completed in 50 days by employing 50 workers. After 25 days only 40% of the work is complete. How many more men are needed to complete the work on time?

Answer is 25

The approach that I followed is -
Let the total work = 50 * 50 = 2500 man days
Work remaining after 25 days = 2500 * 60 / 100 = 1500 man days
Total men required to complete remaining work in next 25 days = 1500/25 = 60
Extra men required = 60 - 50 = 10.

Where am I going wrong?
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by ntamhane » Sat Jul 02, 2011 7:36 pm
Hi apex,
I approached the sum in the following way:
After 25days 60% of the work is remaining
Worker days Work
50 25 0.4
50+x 25 0.6

0.6*25*50=(50+x)*25*0.4

x=25
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by newgmattest » Tue Jul 05, 2011 1:03 am
Hi GMAT Experts,

Can someone help here.

Thanks.
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by casperkamal » Tue Jul 05, 2011 9:28 am
I did it this way..

if 50 people work for 25 days then total work done is 1250 days

this is 40% So 100% 3125 days.

since 1250 days are already complete the remaining days of work to be done is 3125-1250 = 1875

So 1875/25 is 75 men. 50 already employed so 25 to be employed.
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by casperkamal » Tue Jul 05, 2011 9:34 am
Where am I going wrong?
I'm still not very sure. But you can check this. A wall that needs to be completed in 50 days by 50 workers doesn't indicate that it is 2500 man days work.

start from the later point where you say if 50 people work for 25 days then they complete 40% of the work. So it is 1250 days of work.
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by worldpeace93 » Tue Jul 05, 2011 9:47 am
apex231 wrote:A wall has to be completed in 50 days by employing 50 workers. After 25 days only 40% of the work is complete. How many more men are needed to complete the work on time?

Answer is 25

The approach that I followed is -
Let the total work = 50 * 50 = 2500 man days
Work remaining after 25 days = 2500 * 60 / 100 = 1500 man days
Total men required to complete remaining work in next 25 days = 1500/25 = 60
Extra men required = 60 - 50 = 10.

Where am I going wrong?


You are wrong in taking total work = 2500
You have to take it as 40% of work = 25X50
hence remaining work =WR= (60/40)*25X 50
No of men = WR/25=75

hence answer is 25men
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by Buix0065 » Tue Jul 05, 2011 8:37 pm
Hi,

My approach.

There is 100 units of work needed to be done.

50 workers, over 25 days accomplishes 40 units.

In another 25 days, the 50 workers will accomplish another 40.

you need another 20 units completed in that time, which is half of what 50 workers can do, so 50/2 = 25 more workers.
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by GMATGuruNY » Tue Jul 05, 2011 9:07 pm
A wall has to be completed in 50 days by employing 50 workers. After 25 days only 40% of the work is complete. How many more men are needed to complete the work on time?
Since 40% of the work is completed in the first 25 days, 60% must be completed in the remaining 25 days.
Thus, 60-40 = 20 more units must be completed in the remaining 25 days than were completed in the first 25 days.
We need to determine how many workers are needed to complete these 20 additional units.
Since 50 workers can complete 40 units, the number of workers needed to complete 20 units = 25.
The approach that I followed is -
Let the total work = 50 * 50 = 2500 man days
The values above do not satisfy the situation described in the problem.
Although 50 workers are hired to build the wall in 50 days, this number of workers is insufficient: 50 workers can complete only 40% of the wall in 25 days.
If we conclude that work = workers*days = 50*50 = 2500 units, then 50 workers will complete half of the wall in 25 days.

To use this approach:
Let rate per worker = 1 unit per day.
Work completed by 50 workers each day = 50*1 = 50 units.
Work completed over 25 days = 25*50 = 1250 units.

Let w = wall.
Since 1250 units = 40% of the wall:
1250 = .4w
w = 1250/.4 = 3125 units.

Remaining work after 25 days = 3125-1250 = 1875 units.
To be completed in 25 days, number of units each day = 1875/25 = 75.
Since each worker completes 1 unit per day, 75 total workers are needed.
Thus, 75-50 = 25 additional workers are needed.
Last edited by GMATGuruNY on Wed Jul 06, 2011 10:34 am, edited 2 times in total.
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by amit2k9 » Tue Jul 05, 2011 9:24 pm
man hours for 25 days = 25*50 = 1250 (estimated) But actual = 1000.
total man hours required = 50*50 = 2500

thus in 25 days balance man hours = 2500-1000 = 1500

hence 1500/25 = 60.

hence 60-50 = 10 more men required.
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by diebeatsthegmat » Wed Jul 06, 2011 6:47 pm
GMATGuruNY wrote:
A wall has to be completed in 50 days by employing 50 workers. After 25 days only 40% of the work is complete. How many more men are needed to complete the work on time?
Since 40% of the work is completed in the first 25 days, 60% must be completed in the remaining 25 days.
Thus, 60-40 = 20 more units must be completed in the remaining 25 days than were completed in the first 25 days.
We need to determine how many workers are needed to complete these 20 additional units.
Since 50 workers can complete 40 units, the number of workers needed to complete 20 units = 25.
The approach that I followed is -
Let the total work = 50 * 50 = 2500 man days
The values above do not satisfy the situation described in the problem.
Although 50 workers are hired to build the wall in 50 days, this number of workers is insufficient: 50 workers can complete only 40% of the wall in 25 days.
If we conclude that work = workers*days = 50*50 = 2500 units, then 50 workers will complete half of the wall in 25 days.

To use this approach:
Let rate per worker = 1 unit per day.
Work completed by 50 workers each day = 50*1 = 50 units.
Work completed over 25 days = 25*50 = 1250 units.

Let w = wall.
Since 1250 units = 40% of the wall:
1250 = .4w
w = 1250/.4 = 3125 units.

Remaining work after 25 days = 3125-1250 = 1875 units.
To be completed in 25 days, number of units each day = 1875/25 = 75.
Since each worker completes 1 unit per day, 75 total workers are needed.
Thus, 75-50 = 25 additional workers are needed.
hi,
can you please tell me if i do this math correctly?
50 workers do 0.4 job in 25 days
x worker do 0.6 job in 25 days so x=75
so we need 25 more workers to finish the work on time.
can i logically do that? or the solution is wrong?
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