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If 20 men or 24 women or 40 boys can do a job in 12 days [#permalink]
01 Dec 2004, 10:50

If 20 men or 24 women or 40 boys can do a job in 12 days working for 8 hours a day, how many men working with 6 women and 2 boys take to do a job four times as big working for 5 hours a day for 12 days? (1) 8 men (2) 12 men (3) 2 men (4) 24 men

If 20 men or 24 women or 40 boys can do a job in 12 days working for 8 hours a day, how many men working with 6 women and 2 boys take to do a job four times as big working for 5 hours a day for 12 days? (1) 8 men (2) 12 men (3) 2 men (4) 24 men

Mmm...a tough one. I can only come up the following though, need someone else to show me the light!

Let x, y, z be the portion of a job a man, a woman and a boy does. Let k be the number of man required for the second job.

20/x + 24/y + 40/z = 1

My logic is (# of man) * the potion of the job a man can do + (# of woman) * the potion of the job a woman can do + (# of boy) * the potion of the job a boy can do

Same idea apply to the second job

k/x + 6/y + 2/z = 1

Now I am stuck here. I do not know how to incorporate the days and hours into the equation.

I think the answer choices may be wrong...Here's my logic

a) looking at the ratios, we get that 2 boys is equal to 1 men (interms of the rate at which they work)
b) 6 Women by the same above logic equals only 5 men working
c) now, the question is 6W + 2B + XMen to complete a job 4 times as big and at lesser no. of hours per day.
d) that is equivalent of saying 6M (2B + 6 women = 6Men) + X Men.
e) 20 Men take 96 manhours (12days *8hrs/day) to doing that job. So, 4 times that job would take 80 men.
f) We already have 6M equivalent work contributed by 2boys and 6 women. So, it will take remaining 74 men (80-6) to doing 4 times the job @8hrs /day.
g) So, if the number of hrs/day is going to be be only 3 hrs, then the no. fo days will increase by 8/5 times (8/5 is derive from 96/60).

In a nutshell, the it will be surely more than the 24 men mention in the answer choice.

Ok I think I am right in my earlier approach which was completely intuitive. However, I luckily read one more interesting method that works well too...

Important to note this: More work, More men needed; Fewer Hours, More Men needed;Fewer days, More Men needed.

ok, lets draw something for easy working

Men Days hours Job
20 12 8 1
x 12 5 4

x= 20*(12/12)*(8/5)*(4/1) = 128 M

As said earlier in my other post...6W and 2Boys equal 6men. So, we need 128-6= 122 men.

1 job takes 20 men 12days at 8 h per day = 1 job takes 20 men 96 h. Therefore the fraction of job done by 1 man in 1 hour is 1 / (20 * 96) (units are job / (man *h)).

Following the same reasoning:
1/(24*96) (jobs / woman*h))
1/(40*96) (jobs / boy*h))

We now know the fraction of job per type of person in 1 h.

The new job will be 4 (original) jobs in 12 * 5 = 60 hours

I used the following equation:

Job/ h = fraction of job per hour done by 2 boys + fraction of job per hour done by 6 women + fraction of job per hour done by X men

It takes 96 hours for 20 men or 24 women or 20 boys to complete the first job. This means that as far a productivity goes, 1 man = 6/5 women = 2 boys. [1.1]

We have to think in terms of man-hours here.
The number of man-hours required of 1 man to complete the first job = 4 * the number of hour required of one man to complete the new job

hence we have,

20men * 96hours = number of men required * 60 hours * 4
It yields
number of men required = 8
But there are 6 women and 2 boys working on the job. Using 1.1 we can say that, 6 men (6 women = 5 men and 2 boys = 1 man) working on the new job is equivalent to 6 women and 2 boys working on the job.

Hence we need 2 extra blokes to help 6 women and 2 boys out.

20men * 96hours = number of men required * 60 hours * 4

Oxon,
Sorry I dont understand this part.

Even if we take manhours, if 20 Men can complete a job in 96 hours, It needs 80 men to complete a job that is 4 times bigger. Am I getting caught with only one view? Pls advise.

Surprisingly, If the question were to read '4 times smaller in size of the original job' then the answer is 2.

The 'x' in my previous post would be = 20*(12/12)*(8/5)*(1/4) = 8 Men.
2 boys and 6 women = 6 Men. SO, total men needed is 8-6 = 2.

In my first attempt I got 122 men. Then, I noticed the following:
- The new job if 4 times as big as the first one. How could one the number of adult male workers required be less than 20 given that?
a. they reduced the number of women and boys workers.
b. All have less time to complete the task 60 hours vs. 96 hours.

Surely the new job is 4 times as small as the first one. This is why I stated in my post the following:
The number of man-hours required to complete the first job = 4 * the number of hour required to complete the new job
hence,
20 * 8 * 12 = number of man hours to complete the new job (adult male workers only) * 5 * 12 * 4

so yeah, basically there is typo in the question stem and 122 men is the correct answer to the question.

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