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Four workers can dig a ditch in 42 days. They begin

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by emdadul28 » Sun Dec 04, 2016 6:00 pm
Four workers can dig a ditch in 42 days. They begin the work, but one worker work only 12 days. How long will it take to complete the job?
A contract is to be completed in 56 days and 104 men were set to work, each working 8 hours a day. After 30 days, 2/5 of the work is completed. How many additional men be employed, so that the work may be completed in time if each man works 9 hours a day?
Can anyone help with these two math by following same procedure. Thank in advance.
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by GMATGuruNY » Mon Dec 05, 2016 4:14 am
Moving forward, please post each question in a separate thread.
There is typo in the first problem.
It should read as follows:
emdadul28 wrote:
Four workers can dig a ditch in 42 days. They begin the work, but one worker works only 1/2 days. How long will it take to complete the job?
Let the rate for each full-time worker = 2 units per day, implying that the rate for 4 full-time workers = 4*2 = 8 units per day.
In 42 days, the amount of work produced by 4 full-time workers = rt = 8*42 = 336 units.
Rate for 3 full-time workers and 1 half-time worker = (3*2 + 1) = 7 units per day.
To produce 336 units, the time required by 3 full-time workers and 1 half-time worker = w/r = 336/7 = 48 days.
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by GMATGuruNY » Mon Dec 05, 2016 5:12 am
I believe that the following reflects the intent of the problem:
A job is to be completed by 104 men, each working at a constant rate for 8 hours per day. After 30 days, 2/5 of the job is completed. If each man increases his time per day to 9 hours, how many additional men must be employed to complete the remainder of the job in 26 days?
We can use the following formula:

(number of workers)(hours per day)(number of days)/output = (number of workers)(hours per day)(number of days)/output

Let the job = 5 units, implying that 2 of the units are completed in the first 30 days and that the remaining 3 units must be produced in the final 26 days.
Let x = the number of workers required to produce the remaining 3 units in 26 days.

104 men working 8 hours per day for 30 days produce 2 units.
We want to determine how many workers are required to produce 3 units in 26 days if the number of hours per day is increased to 9.
Plugging these values into the formula above, we get:

(104)(8)(30)/2 = (x)(9)(26)/3

Solving the resulting equation, we get:
x = 160.

Since the number of workers must increase from 104 to 160, the number of additional workers = 160-104 = 56.
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by Matt@VeritasPrep » Thu Dec 08, 2016 8:28 pm
emdadul28 wrote:Four workers can dig a ditch in 42 days. They begin the work, but one worker work only 12 days. How long will it take to complete the job?
I'm not sure there's a typo here, as the answer is still a round number.

4 workers * 42 days = 168 man-days of work

If the four workers work together for 12 days, they complete 4 * 12 = 48 man-days of work.

That means that 120 man-days are left. 120 man-days / 3 remaining workers = 40 days.

So the job will take 52 days, assuming everyone works each day without taking days off (except for our fourth worker, who disappears after the twelfth day).
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by Matt@VeritasPrep » Thu Dec 08, 2016 8:33 pm
emdadul28 wrote:A contract is to be completed in 56 days and 104 men were set to work, each working 8 hours a day. After 30 days, 2/5 of the work is completed. How many additional men be employed, so that the work may be completed in time if each man works 9 hours a day?
30 days * 8 hours = 240 hours

240 hours * 104 men = 24960 man-hours

If 24960 man-hours = (2/5) of the job, then the job = 62400 man-hours total.

Since we've done 24960, we have 37440 hours left to do.

If we have men working at 9 hours a day, that's 37440 / 9 = 4160 man-days left.

We have 26 actual days, so we need 4160 / 26 = 160 men to finish the job in time. We already have 104, so we need to hire 56 more.
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by Matt@VeritasPrep » Thu Dec 08, 2016 8:33 pm
And a tip of the cap to the author of the second question: it was very clever to have the extra number of men turn out to be the same as the number of days!
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by Arunkumar S » Sun Dec 18, 2016 11:05 am
Always assume total work is 1
4 worker complete work in 42 days
So 1 workers 1 day work is 1/(42*4)=1/168
12(n1) days works for 4 workers is = 4*(1/168)*12 ==> 12/42 ==> 2/7
Balance work = 1-(2/7)= 5/7
1 worker left after 12 days So now we have only 3 workers and 3 workers one day job is 3*(1/168)= 1/56
5/7 = n2*(1/56) ==> n2 = (5/7)*56 =40
So total no of days n =n1+n2
n = 12+40 = 52
Ans = 52
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