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Intern  B
Joined: 27 Jul 2011
Posts: 49
If 6 men can do a piece of work in 30 days of 9 hours each,  [#permalink]

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15 00:00

Difficulty:   15% (low)

Question Stats: 80% (02:16) correct 20% (02:25) wrong based on 248 sessions

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If 6 men can do a piece of work in 30 days of 9 hours each, how many men will it take to do 10 times the amount of work if they work for 25 days of 8 hours?

A. 61
B. 64
C. 84
D. 81
E. 94

CEO  D
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Re: If 6 men can do a piece of work in 30 days of 9 hours each,  [#permalink]

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6
2
smartyman wrote:
If 6 men can do a piece of work in 30 days of 9 hours each, how many men will it take to do 10 times the amount of work if they work for 25 days of 8 hours?

A. 61
B. 64
C. 84
D. 81
E. 94

CONCEPT: $$\frac{(Machine_Power * Time)}{Work} = Constant$$

i.e. $$\frac{(M_1 * T_1)}{W_1} = \frac{(M_2 * T_2)}{W_2}$$

i.e. $$\frac{[6 * (30*9)]}{W} = \frac{[M_2 * (25*8)]}{(10*W)}$$

i.e. $$M_2 = 81$$

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Director  B
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Re: If 6 men can do a piece of work in 30 days of 9 hours each,  [#permalink]

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1
2
smartyman wrote:
If 6 men can do a piece of work in 30 days of 9 hours each, how many men will it take to do 10 times the amount of work if they work for 25 days of 8 hours?
A. 61
B. 64
C. 84
D. 81
E. 94

Amount of work done by 6 men working 30 days working 9 hrs each = 30 * 9 * 6
Let the number of people required for the 2nd case = X

Then X * 25 * 8 = 30 * 9 * 6 * 10
= > X = 81 - Option D)
Veritas Prep GMAT Instructor V
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Re: If 6 men can do a piece of work in 30 days of 9 hours each,  [#permalink]

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1
smartyman wrote:
If 6 men can do a piece of work in 30 days of 9 hours each, how many men will it take to do 10 times the amount of work if they work for 25 days of 8 hours?

A. 61
B. 64
C. 84
D. 81
E. 94

Or you can do it using joint variation:

Number of men required = 6 * (30/25) * (9/8) * 10 = 81

Check this link to see how to solve such questions: http://www.veritasprep.com/blog/2013/02 ... variation/
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Re: If 6 men can do a piece of work in 30 days of 9 hours each,  [#permalink]

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Can someone please explain any other method, preferably the w=rt method. Work rate problems always seem so simple but I always go wrong or am stuck. I was not able to grasp it even after going through the two approaches. Thank you.
Director  S
Joined: 17 Dec 2012
Posts: 623
Location: India
If 6 men can do a piece of work in 30 days of 9 hours each,  [#permalink]

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In this type of problems, converting for unit values will make it easy to solve.

Take a look at the first sentence. We can say, to do the work in 1 day of 9 hours each will take 6*30 men.
To do the work in 25 days will take (6*30) /25 men
Similarly adding the info, that to do the work in a day of 8 hours instead of 9 hours each will take (6 *30*9)/ (25*8) men
To do 10 times the amount of work will take 10 * (6*30*9) / (25*8) = 81 men
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Re: If 6 men can do a piece of work in 30 days of 9 hours each,  [#permalink]

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If 6 men can do a piece of work in 30 days of 9 hours each, how many men will it take to do 10 times the amount of work if they work for 25 days of 8 hours?

A. 61
B. 64
C. 84
D. 81
E. 94

6*30*9=1620 total man hours to do work
let m=number of men needed
m*25*8*1/1620=10
m=81 men
D.
Senior SC Moderator V
Joined: 22 May 2016
Posts: 3729
If 6 men can do a piece of work in 30 days of 9 hours each,  [#permalink]

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smartyman wrote:
If 6 men can do a piece of work in 30 days of 9 hours each, how many men will it take to do 10 times the amount of work if they work for 25 days of 8 hours?

A. 61
B. 64
C. 84
D. 81
E. 94

One version of the rate formula approach . . .
Use standard W = RT formula, but add (# of workers or machines) to R*T, thus: W = #*R*T

Work = (# of workers) * individual rate * time

Scenario 1

Get individual rate from first scenario, where t = (30 * 9hrs = 270 hrs)

Work = # * r * t

1 = 6 * ?? * 270

1 = r * 1620

r = $$\frac{1}{1620}$$

Scenario 2

At that rate, how many men will it take to do 10 times the amount of work if they work for 25 days of 8 hours?
t = (25 * 8 hrs = 200 hrs)

Work = # * r * t

10 = ?? * $$\frac{1}{1620}$$ * 200

10 = # * $$\frac{200}{1620}$$

# of workers = $$\frac{10}{(\frac{200}{1620})} =$$

# of workers =$$(10 * \frac{1620}{200})=(\frac{1620}{20})=\frac{162}{2}= 81$$

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Target Test Prep Representative V
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Re: If 6 men can do a piece of work in 30 days of 9 hours each,  [#permalink]

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smartyman wrote:
If 6 men can do a piece of work in 30 days of 9 hours each, how many men will it take to do 10 times the amount of work if they work for 25 days of 8 hours?

A. 61
B. 64
C. 84
D. 81
E. 94

The hourly rate of the 6 men is 1/(30 x 9) = 1/270. If we let x = the number of men needed to do 10 times the work when they work for 25 days of 8 hours, then the hourly rate of these x men must be 10/(25 x 8) = 10/200 = 1/20. We can create the following proportion and solve for x:

6/(1/270) = x/(1/20)

1620 = 20x

x = 1620/20 = 81

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Intern  B
Joined: 28 Sep 2011
Posts: 14
Location: India
GMAT 1: 640 Q47 V31 GMAT 2: 640 Q47 V31 GPA: 3
If 6 men can do a piece of work in 30 days of 9 hours each,  [#permalink]

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The best way to tackle any of these problems is to follow this sequence (be it any question)

No. of workers ----- Time ----- work
6 ----- 30x9 hrs ----- 1

we need to find:

? ----- 25x8 ----- 10

so, by unitary method:

6 ----- 1 ----- 1/ (30x9)

1 ----- 1 ----- 1/ (30x9)*(6)

1 ----- 25x8 ----- 25x8/ (30x9)*(6)

so,

{(10)* (30x9)*(6)/ (25x8)} ----- 25x8 ----- 10
=81 If 6 men can do a piece of work in 30 days of 9 hours each,   [#permalink] 29 Nov 2019, 06:35
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