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If 6 men can do a piece of work in 30 days of 9 hours each,

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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


Please help explains using rates formulae as I could not get the answer. Thanks
[Reveal] Spoiler: OA
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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


Please help explains using rates formulae as I could not get the answer. Thanks


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)
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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


Please help explains using rates formulae as I could not get the answer. Thanks


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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New post 18 Jul 2014, 04:21
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.
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If 6 men can do a piece of work in 30 days of 9 hours each, [#permalink]

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New post 18 Jul 2014, 04:38
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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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


Please help explains using rates formulae as I could not get the answer. Thanks


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. \(M_2 = 81\)

Answer: option 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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New post 25 Sep 2016, 13:06
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
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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

Please help explains using rates formulae as I could not get the answer. Thanks

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 =\((10 * \frac{1620}{200})=(\frac{1620}{20})=\frac{162}{2}= 81\)

Answer 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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New post 01 Dec 2017, 07:49
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

Answer: D
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Re: If 6 men can do a piece of work in 30 days of 9 hours each,   [#permalink] 01 Dec 2017, 07:49
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