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# A contractor hires 100 men to finish a job in 50 days. After 14 days,

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Manager
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A contractor hires 100 men to finish a job in 50 days. After 14 days, [#permalink]

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05 Oct 2014, 07:57
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75% (hard)

Question Stats:

66% (02:35) correct 34% (03:38) wrong based on 300 sessions

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A contractor hires 100 men to finish a job in 50 days. After 14 days, n men leave. After some more days, the contractor hires 2n more men to complete the job on time. For how many days did these 2n men work?

A. 20
B. 18
C. 16
D. 12
E. 8
[Reveal] Spoiler: OA

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Re: A contractor hires 100 men to finish a job in 50 days. After 14 days, [#permalink]

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05 Oct 2014, 08:26
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Step1: Find Each day what % of work is finished ; it requires 50 days to complete which means each day 1/50= 2% work will be completed.
Step 2 : After 14 Days = 14* 2= 28% of work is finished. remaining is 72% ( which means if same 100 men were about to complete the job they would have required 36 more days)
Step3: Let us assume all people have left job. therefore contractor hires 2n people. initially it was taking 36 days to compete for n people. at present 2n people are present to finish job. hence 18 more days.
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Re: A contractor hires 100 men to finish a job in 50 days. After 14 days, [#permalink]

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05 Oct 2014, 08:59
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Solution 1
Suppose a job is to make 5000 details. So 1 men in 1 day can do $$5000/100*50=1$$ detail.

After 14 days they make 14*100=1400 details.

After $$x$$ more days they do $$1400+x\cdot (100-n)$$ details. So, we have $$5000-1400-x(100-n)=3600-x(100-n)$$ details to do and $$50-14-x=36-x$$ days.

We have an equation: $$3600-x(100-n)=(36-x)*(100-n+2n)$$

$$3600-100x+xn=3600+36n-100x-xn$$

$$2xn=36n$$

$$x=18$$

So, these $$2n$$ men work for $$36-18=18$$ days.

Solution 2
After 14 days we have 36 days to finish the work. And after $$x$$ more days we didn't do $$x\cdot n$$ details, because $$n$$ people leave the work.

To make everything on time we hire $$2n$$ people or just $$n$$ people more to finish the undone work in $$36-x$$ days. So, $$x\cdot n=(36-x)\cdot n$$ or $$x=18$$.

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Re: A contractor hires 100 men to finish a job in 50 days. After 14 days, [#permalink]

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08 May 2015, 21:28
Total work by 50 days =50*100=5000units
Work done for 14 days=14*100=1400units
WOrk remaining=3600units
The remaining work is done as follows----- {(100-n)*(36-x)---n being no. of workers left job and x ,no. of days work done by 2n men and 36 no. of days left} + {(100+n-2n)*x }
equating the above to 3600 yields 18 as our answer
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Re: A contractor hires 100 men to finish a job in 50 days. After 14 days, [#permalink]

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14 Apr 2016, 13:17
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First attempt took 6 mins long. I believe it's because I was confused about how many days in total this job took even after making changes.

The rate of each worker is (1/5000).

After 14 days, 3600/5000 of the job is left.

If x = some days that 100 - n workers worked for,

3600 = (100 - n) x + (100 - n + 2n) (36 - x)

This will result in x = 18. 36 - 18 = 18. So, it took 18 days to complete the job with 2n additional workers.
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Re: A contractor hires 100 men to finish a job in 50 days. After 14 days, [#permalink]

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04 May 2016, 02:41
A contractor hires 100 men to finish a job in 50 days. After 14 days, n men leave. After some more days, the contractor hires 2n more men to complete the job on time. For how many days did these 2n men work?

A. 20
B. 18
C. 16
D. 12
E. 8

Let us say that "n = 1". Also, let us assume that "some = 1000000".

Therefore, the question should now read as:

A contractor hires 100 men to finish a job in 50 days. After 14 days, 1 man leaves. After 1000000 more days, the contractor hires 2 more men to complete the job on time. For how many days did these 2 men work?

So during those 1000000 days, 99 men were still working, correct? So the work would have been finished before hiring 2 more men. So the 2 men need to work 0 days.

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Re: A contractor hires 100 men to finish a job in 50 days. After 14 days, [#permalink]

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09 May 2016, 00:09
dixitraghav wrote:
A contractor hires 100 men to finish a job in 50 days. After 14 days, n men leave. After some more days, the contractor hires 2n more men to complete the job on time. For how many days did these 2n men work?

A. 20
B. 18
C. 16
D. 12
E. 8

Let us say that "n = 1". Also, let us assume that "some = 1000000".

Therefore, the question should now read as:

A contractor hires 100 men to finish a job in 50 days. After 14 days, 1 man leaves. After 1000000 more days, the contractor hires 2 more men to complete the job on time. For how many days did these 2 men work?

So during those 1000000 days, 99 men were still working, correct? So the work would have been finished before hiring 2 more men. So the 2 men need to work 0 days.

To be able to complete the work in time the contractor needs to hire men before the ones already working complete it (in delayed time). I think this is the unstated and understood part of the question. Extrapolation of given conditions help you arrive at an answer sometimes but not in this case. Liked your line of thought though.
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Re: A contractor hires 100 men to finish a job in 50 days. After 14 days, [#permalink]

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02 Oct 2016, 04:50
A good question by Veritas. Thanks team.
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Re: A contractor hires 100 men to finish a job in 50 days. After 14 days, [#permalink]

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12 Nov 2016, 01:42
2
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A contractor hires 100 men to finish a job in 50 days. After 14 days, n men leave. After some more days, the contractor hires 2n more men to complete the job on time. For how many days did these 2n men work?

A. 20
B. 18
C. 16
D. 12
E. 8

Logical approach..here it goes..

We will do this with the law of averages...
For the first 14 days some work was done..
left days? 36.

Now for some days $$100-n$$ people were working...

after some days $$2n$$ people joined..or in other words..

we then had a total of $$100+n$$ men with us.
We know that every man does the same amount of work everyday(the efficiency is constant).

the same 100 people were there when we had $$n$$ less men, and when we had $$n$$ more men. What comes in your mind? we had to employ $$n$$ more men than usual to make up for the work that we lost when we had exactly $$n$$ less men. These days have to be the same..why? because if we have these $$n$$ extra than usual(100 men) men work for more days than when we had $$n$$ less men, then we will have more than needed work done, and vice versa.

This brings us to think that there were less men and more men for the same number of days..which is?

36/2 = 18 days

(B)

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Re: A contractor hires 100 men to finish a job in 50 days. After 14 days, [#permalink]

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24 Jul 2017, 09:36
smyarga wrote:
Solution 1
Suppose a job is to make 5000 details. So 1 men in 1 day can do $$5000/100*50=1$$ detail.

After 14 days they make 14*100=1400 details.

After $$x$$ more days they do $$1400+x\cdot (100-n)$$ details. So, we have $$5000-1400-x(100-n)=3600-x(100-n)$$ details to do and $$50-14-x=36-x$$ days.

We have an equation: $$3600-x(100-n)=(36-x)*(100-n+2n)$$

$$3600-100x+xn=3600+36n-100x-xn$$

$$2xn=36n$$

$$x=18$$

So, these $$2n$$ men work for $$36-18=18$$ days.

Solution 2
After 14 days we have 36 days to finish the work. And after $$x$$ more days we didn't do $$x\cdot n$$ details, because $$n$$ people leave the work.

To make everything on time we hire $$2n$$ people or just $$n$$ people more to finish the undone work in $$36-x$$ days. So, $$x\cdot n=(36-x)\cdot n$$ or $$x=18$$.

hi

the solution 1 is beautifully done...

anyway, would you please speak something more about solution 2....? Is it not such that, since it is assumed that the work was completed on time, then (36-x)*2n = the remaining job..? So how can this expression equals x*2n....?

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Re: A contractor hires 100 men to finish a job in 50 days. After 14 days, [#permalink]

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24 Jul 2017, 10:05
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Total job = $$100m*50d = 5000md$$ ($$md$$=man-days)

Job done in 14 days = $$100m*14d = 1400md$$. Remaining job = $$5000md - 1400md = 3600md$$.

Let the number of days that $$(100-n)$$ men worked be $$k$$, then $$(100-n)*k + (100+n)*(50-14-k) = 3600$$.

$$100k - nk + 3600 - 100k + 36n - nk = 3600$$.

$$36n - 2nk = 0$$

$$2nk = 36n$$

$$k = \frac{36}{2} = 18.$$

So, the $$2n$$ men worked for $$(36-18) = 18$$ days.
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Re: A contractor hires 100 men to finish a job in 50 days. After 14 days, [#permalink]

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26 Jul 2017, 16:37
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Expert's post
A contractor hires 100 men to finish a job in 50 days. After 14 days, n men leave. After some more days, the contractor hires 2n more men to complete the job on time. For how many days did these 2n men work?

A. 20
B. 18
C. 16
D. 12
E. 8

We are given that 100 men will finish a job in 50 days; thus, the rate of the 100 men is 1/50 and the rate of each man is (1/50)/100 = 1/5000.

This is what we know:

The 100 men work for the first 14 days. Then n men leave and the (100 - n) men work for some number of days. Then 2n men join in (so now there are 100 - n + 2n = 100 + n men) and they all work for the remaining days and complete the job on time, in 50 days.

If we let x = the number of days the (100 - n) men work (after the first 14 days but before the 2n men join in), then (100 + 2n) men (after the 2n men join in) work for (36 - x) days, since the total number of days for the job is still 50. Thus, we can create the following equation:

100(1/5000)(14) + (100 - n)(1/5000)(x) + (100 + n)(1/5000)(36 - x) = 1

The 1 on the right-hand side of the equation represents the complete job and each of the addends on the left-hand side represents the fraction of the job the 100 men, (100 - n) men, and (100 + n) men contribute at different stages of the job, respectively.

Multiplying the equation by 5000, we have:

100(14) + (100 - n)(x) + (100 + n)(36 - x) = 5000

1400 + 100x - nx + 3600 - 100x + 36n - nx = 5000

5000 + 36n - 2nx = 5000

36n = 2nx

36 = 2x

18 = x

Since the extra 2n men actually work (36 - x) days, they work 36 - 18 = 18 days.

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Re: A contractor hires 100 men to finish a job in 50 days. After 14 days, [#permalink]

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30 Jul 2017, 10:36
Here is my solutions -

Please let me know if i am doing anything wrong!!!
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Re: A contractor hires 100 men to finish a job in 50 days. After 14 days, [#permalink]

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03 Oct 2017, 21:19
Let, the 2n people were hired d days after the n people leave.

nd=n(36-d)
d=36-d
d=18

This is so, because half of the 2n people will work just to cover the gap created by the leave of the n people.
Re: A contractor hires 100 men to finish a job in 50 days. After 14 days,   [#permalink] 03 Oct 2017, 21:19
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