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# If 15 men or 24 women or 35 boys do a piece of work in 12

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Manager
Joined: 24 Jan 2005
Posts: 217
Location: Boston
If 15 men or 24 women or 35 boys do a piece of work in 12 [#permalink]

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19 Mar 2005, 10:21
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If 15 men or 24 women or 35 boys do a piece of work in 12 days working 8 hrs a day, how many men must be associated with 12 women and 6 boys to do another piece 9/2 times as great in 30 days working 6 hrs a day

(a) 8 men
(b) 10 men
(c) 12 men
(d) 4 men
(e) 15 men
Senior Manager
Joined: 15 Mar 2005
Posts: 418
Location: Phoenix
Re: PS Mern at work [#permalink]

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19 Mar 2005, 12:07
anirban16 wrote:
If 15 men or 24 women or 35 boys do a piece of work in 12 days working 8 hrs a day, how many men must be associated with 12 women and 6 boys to do another piece 9/2 times as great in 30 days working 6 hrs a day

(a) 8 men
(b) 10 men
(c) 12 men
(d) 4 men
(e) 15 men

I am getting a wrong answer - maybe the aproach is wrong, or some calculation mistake. Can someone please point out?

------------------
Rate of work of men : women: boys = 1/15:1/24:1/35
1 man = 8/5 women = 7/3 boys.
1 woman = 5/8 men, 1 boy = 3/7 men.

First work = 15*12*8 man hours = 1440 man hours

Second work = 9/2 * 1440 = 720*9 = 6480 man hours.

Workforce = 12 women + 6 boys = 15/2 + 18/7 men = 141/14 men

Time = 180 hours

If additional men required = x, then

(141/14 + x) 180 = 6480

141/14 + x = 648/18 = 36

x is approx 26.
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VP
Joined: 18 Nov 2004
Posts: 1433

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19 Mar 2005, 12:56
"A"

If x is number of men for the ques then

women doing the job alone in the second case will take = ((96*24)/12)9/2
= 96*9 hrs

similarly for boys = ((96*35)/6)9/2 = 9*8*35
similarly for men = ((96*15)/X)9/2

9/2 = 180/96*9 + 180/9*8*35 + 180*2X/96*15*9

X = 7.9 ~ 8... don't know if it is right
Manager
Joined: 05 Feb 2005
Posts: 116
Location: San Jose

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19 Mar 2005, 13:20
I also got 26! Must be an ill formed question.

If 15 men or 24 women or 35 boys do a piece of work in 12 days working 8 hrs a day, how many men must be associated with 12 women and 6 boys to do another piece 9/2 times as great in 30 days working 6 hrs a day

(a) 8 men
(b) 10 men
(c) 12 men
(d) 4 men
(e) 15 men

First piece of work = 15x12x8 man hours = 24x12x8 woman hours = 35x12x8 child hours

Second piece of work = 9/2 x 15x12x8 man hours
= A x 30 x 6
where A is the number of men, if the group composed of only men.

A = 36 men

Lets compute the ratios:
1 woman = 15/24 man
1 child = 15/35 man

So 12 women + 6 boys = 12x15/24 + 6x15/35 = 141/14 = 10.08

Number of men needed = 36 - 10.08 = 26
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Anyone who has never made a mistake has never tried anything new. -Albert Einstein.

Manager
Joined: 24 Jan 2005
Posts: 217
Location: Boston

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20 Mar 2005, 16:33
My mistake, a typo extremely sorry for wasting your time.
It is 2(1/4) or 2.25 times the work (NOT 9/4). Now you'd get 8.
Sorry again
20 Mar 2005, 16:33
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# If 15 men or 24 women or 35 boys do a piece of work in 12

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