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Twenty-four men can complete a work in sixteen days.Thirty-two women c

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mbafinhopeful

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14 Jan 2018, 19:00

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Chemerical71

Total work \(= 24m*16d = 384md\), or \(32w * 24d = 768wd\).

\(24m * 16d = 32w * 24d\)
\(1md = 2wd\): men are twice as efficient as women.

Work done by \(16m\) and \(16w\) in \(12\) days \(= 12(32wd + 16wd) = 576wd\).

Remaining work \(= 768-576 = 192 wd\), can be completed in \(2\) days by \(\frac{192}{2} = 96w\).

\(96w - 48w = 48w = 24m\). Ans - B.

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Abhishek009

Chemerical71

Quote:

Twenty-four men can complete a work in sixteen days.

So, Total mandays = 24*16 => 384

Quote:

Thirty-two women can complete the same work in twenty-four days.

So, Total womandays = 32*24 => 768

Now, total work = LCM( 384,768 ) => 768

So, Efficiency of men = 2 & Efficiency of women = 1

Quote:

Sixteen men and sixteen women started working for twelve days.

Work completed = (16*2 + 16*1 )12 => 576 units , Work left = 768 - 576 => 192

Quote:

How many more men are to be added to complete the work remaining work in 2 days?

\({(16+m)*2 + 16*1 }*2 = 192\)

Or, \((16+m)*2 + 16 = 96\)

Or, \((16+m) = 40\)

Or, \(m = 24\)

Thus, we need to add , 24 more men workers, answer must be (B) 24 men...

{(16+m)*2 + 16*1 }*2 = 192
Why have you not multiplied mans efficiency here?

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24m*16=32w*24
m=2w
16m+16w=48w
48w 12 dasy works =12*48/32*24
=3/4
the rest =1/4
1/4 works in 2 days need
=48*12*4/3*4*2
=96 w
2w = 1 m
96w=48 m
here original m 24
so extra m 48-24
24

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Chemerical71

Nice problem!

Let´s suppose each man does 1 task/day , and each woman does k tasks/day (where k>0, not necessarily an integer).

By the question stem, we know that:

> 24 men do 1 work in 16 days, hence 1 work = 24*16 tasks (1)
> 32 women do 1 work in 24 days, hence 1 work = 32*24*k tasks implies, by (1) above, that k = 1/2

> 16 men and 16 women will do in 12 days exactly 16*12*1 + 16*12*1/2 = 24*12 tasks, therefore by (1) we have still 24*(16-12) = 24*4 tasks to be done.

> If x is the number of men to be added (our FOCUS), we have a group of (16+x) men and 16 women performing (16+x)*1 + 16*1/2 = (24+x) tasks/day,
and the final touch is done with UNITS CONTROL, one of our method´s most powerful tools:

\(24 \cdot 4\,\,\,{\text{tasks}}\,\,\, = \,\,2\,\,days\,\,\left( {\frac{{24 + x\,\,\,{\text{tasks}}}}{{1\,\,\,{\text{day}}}}\,\,\,\begin{array}{*{20}{c}}\\
\nearrow \\ \\
\nearrow \\
\end{array}} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,24 + x = 24 \cdot 2\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = x = 24\)

Obs.: arrows indicate licit converters.

(If you realize this solution is absolutely clear and safe, you are the perfect candidate for our method... try our free and super-complete test drive!)

This solution follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.

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10 Nov 2018, 21:16

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24 men will take 16 days.
1 man will take 384 days.
32 women will take 24 days.
1 women will take 768 days.

Therefore, 1 women's work rate is equal to 0.5 man.

16 man + 16 women = 24 man.
So, they will require 4 more days with the same manpower. If they double the manpower they can complete the work in 2 days.

Therefore, another 24 men are required.

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20 Jun 2019, 19:15

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ScottTargetTestPrep

Chemerical71

We are given that the rate of 24 men is 1/16, so the rate of each man is (1/16)/24 = 1/(16 x 24). Similarly, we are given that the rate of 32 women is 1/24, so the rate of each woman is (1/24)/(32) = 1/(24 x 32). Now we can find the fraction of the job that is completed by 16 men and 16 women in one day.

16 x 1/(16 x 24) + 16 x 1/(24 x 32)

1/24 + 1/(24 x 2)

2/48 + 1/48

3/48 = 1/16

We see that 16 men and 16 women can complete 1/16 of the job in one day, so they can complete 12 x 1/16 = 12/16 = 3/4 of the job in 12 days.

We can let m be the number of additional men who must be added to complete the job in two more days. Since we have 1 - 3/4 = 1/4 of the job left and it needs to be completed in two2 more days, each day they need to complete (1/4)/2 = 1/8 of the job. Thus, we can create the following equation to solve for m:

(16 + m) x 1/(16 x 24) + 16 x 1/(24 x 32) = 1/8

1/24 + m/(16 x 24) + 1/48 = 1/8

Multiplying the above equation by 48, we have:

2 + m/8 + 1 = 6

m/8 = 3

m = 24

Answer: B

Hi ScottTargetTestPrep

Thank you for this detailed equation, I need u to correct me where did I go wrong.

So I found the rate of man and woman, as derived by you. But the final equation which I formed was:

16+x/16*24 + 16/24*36= 1/14

Where x is the additional men required to complete the work in 2 more days which makes it 12 days + 2 more days

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05 Jul 2020, 17:22

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Chemerical71

24 man can complete in 16 days
16 man can complete in 24/16 * 16 days or, 24 days

32 women >>>> 24 days
16 women>>>> 48 days

So, in 12 days work completed by 16 men and 16 women = (1/24+1/48)*12= 12*3/48= 3/4
For remaining 1/4 work, it would have take 12/3 = 4 days in current setting.
Since 1 man = 2 women...we can say, 16 + 8 = 24 men need 4 days to finish the 1/4 part of work.

4 days>>>> 24 men
2 days >>>>>24 * 2 men
There is already 24 men, so we need 24 more.

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Chemerical71

time taken by 16 men=24 days
time taken by 16 women = 48 days

Proportion of work completed by 16 men and 16 women in 12 days= 12 /24 +12/48

In 14 days work is complete

(12+2)/24 + (12+2) /48 + 2/(16*24)/x =1 ( 16 men take 24 days . So x men take 16*24/x days. proportion of work completed by the additional men in 2 days = 2/ (16*24)/x )

7/8 + x/192 =1

x=24

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24 Men can do the work in 16 days. ie; 24*16 man-day work
32 Women can do the work in 24 days. ie; 32*24 women-day work.

comparing first two lines, 1M-work=2W-work.

16 Men and 16 Women have done the work for 12. So we can say 24 men have done the work for 12 days.

So total amount of work done, 24*12 Man-day work. So, remaining work 24*4 Man-day work.

So, to complete the remaining work in 2 days we need (24*4)/2=48 Men.

We have already 24 Men equivalence, we need another 48-24= 24 days.

I hope this works.

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Chemerical71

I like to approach work problems with the LCM method-
24M-16 Days
32W- 24 Days

Looking at the numbers, lets say 96 jobs is the amount of work to be done. (For easy divisibility)
24 M work at a rate of 6 jobs per day (96/16)
32 W work at a rate of 4 jobs per day (96/24)

16 M work at a rate of 4 jobs per day [(6/24)X16]
16 W work at a rate of 2 jobs per day

Working together they work 6 jobs per day so in 12 days they complete 72 jobs.
in the next 2 days they will complete 12 jobs more adding up to 84 Jobs.

Now we just need to find the Men required to do the balance job i.e. 12 jobs (96-84) in 2 days.
We already know that 24 M work at a rate of 6 jobs per day.

Hence 24 men will do 12 jobs in 2 days which is our answer.

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Crazy Numbers, but one little trick I've seen followed by the Top Contributors......don't Multiply trough Crazy Numbers Until you Absolute have to!

(1st) Find the Rate of 1 MAN and the Rate of 1 WOMAN

Rate of 24 Men = 1 job / 16 Days

Rate of 1 Man = 1 job / (16 * 24) Days

Rate of 32 Women = 1 job / 24 Days

Rate of 1 Woman = 1 job / (24 * 32) Days

(2nd) Find out How much Work is REMAINING after 16 Women and 16 Men work for ---- 14 DAYS, not 12 Days

*Let me explain: No matter how many more Men we hire, these 16 Women and 16 Men who started are going to be contributing their work in the Extra 2 Days that we need to Finish the Work. So, we need to figure out how much Work Remains after:

(1)Both groups work for 12 days together

and

(2)Both groups work with the X - NEW MEN for 2 more Days

Since there are NO Economies of Scale and Each participant adds their own work Independently, we can find the amount of work that the 2 Groups contribute throughout these 18 Days.

The Extra MEN we will need will have to complete the REMAINING Work in 2 Days given the Rate per 1 MAN we found above.

Using the Following Matrix

# of Men/Women * (Rate per 1 Man OR Rate per 1 Woman) * (Time working) = WORK Contributed

(16 Men) * (1 / 24*16) * (14 Days) = A

(16 Woman) * (1 / 24*32) * (14 Days) = B

A Work contributed by the 16 Men = 28/48 of Job

B Work Contributed by the 16 Women = 14/48 of Job

Total Work COMPLETED before we hire MORE Men = 42/48 = 7/8

Work REMAINING for the MORE Men we hire = 1 Job - (7/8 Completed) = 1/8 of Job

(3rd) Determine How many More MEN we need to hire when the Rate of 1 MAN = 1 / (24 * 16) (job/per day)

Let the # of Men we need = M

M * (Rate of 1 Man) * (2 Days Deadline) = 1/8 of Job Remaining to be Completed

M * (1 / 24*16) * (2) = 1/8

2M / 24*16 = 1/8

---cross-multiplying-----

16M = (24) * (16)

M = 24 Men needed to finish the work in 2 Days

-B-

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Not to sound misogynistic, but let's convert everything to MAN-DAYS.

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Let total work be LCM of 16 and 24 which is 48 units

so 24M rate is 1/16 so they can do 48/16 i.e. 3 units of work per day (this is for 24 men)
same way rate if 32W rate is 1/24, so they can do 48/24 i.e. 2 units of work per day

now we have 16M + 16W .. their combined rate is:
24M is 3 Units
so 16 men is 16x3/24 i.e. 2 units

so combined rate is 2+1 is 3 units

now in 12 days they will do 3x12 i.e. 36 units of work.
Work left 48 - 36 i.e. 12

now these people will only be able to do half of the work in 2 days (3x2)
But we need more men to complete 3 units of work per day for next 2 days to complete 6 units of work left
so 3 units we already know is 24 .. so we need 24 extra Men .. B

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24 men x 16 days = 1 work
=> 1 men x 1 day = 1/(24*16) work (1)

32 women x 24 days = 1 work
=> 1 women x 1 day = 1/(32*24) work (2)

From (1) => 16 men x 12 days did (16*12)/(24*16) = 1/2 work
From (2) => 16 women x 12 days did (16*12)/(32*24) = 1/4 work
After 12 days, 16 men + 16 women did 3/4 work

For the next 2 days, WITHOUT any additional men, 16 men + 16 women did an additional 3/4 / 12 * 2 = 1/8 work
So the work left for addional men to work is 1 - 3/4 - 1/8 = 1/8 work in 2 days
So the work left for additional men to work in 1 day is 1/16 work
1 men in 1 day did 1/(24*16) work, so we would need 24 men to do 1/16 work
=> 24 men

Hope this helps

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Chemerical71

let work done per day by one man = M, work done per day by on woman = W

that total work = 24 * M * 16 = 32 * W * 24 => 384 M
=> M = 2 * W

Work completed in 12 days = (16 * M + 16 * W) * 12 = (16 * M + (8 * M )) * 12 = 288 M
Work remained = 96 M

let x be additional men required to complete work in 2 days.

96 M = (16 + x + 8) M * 2
x = 24

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Twenty-four men can complete a work in sixteen days.Thirty-two women can complete the same work in twenty-four days.Sixteen men and sixteen women started working for twelve days.

How many more men are to be added to complete the work remaining work in 2 days?

Man-days required to complete the work = 24*16 = 384 man-days
Women-days required to complete the work = 32*24 = 768 women-days

384 man-days = 768 women-days
1 man-day = 2 women-day

Sixteen men and sixteen women started working for twelve days.
Man-days = 16*12 + 16*12/2 = 288 man-days

Remaining Man-days = 384 - 288 = 96 man-days
Days = 2
Men required = 96/2 = 48 men
Existing men equivalent = 16 + 16/2 = 24 men
Men to be added = 48 - 24 = 24 men

IMO B

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