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

Question

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

GMATinsight · Accepted Answer

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{ }{W} = \frac{ }{(10*W)}

i.e.   M_2 = 81

Answer: option D

kinjiGC · Answer

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)

KarishmaB · Answer

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: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2013/02 ... variation/

suhaschan · Answer

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.

SVaidyaraman · Answer

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

gracie · Answer

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.

generis · Answer

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

ScottTargetTestPrep · Answer

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

varun2209 · Answer

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

GmatWarrior700 · Answer

Used a different method here not sure if its correct please validate

6m x 9hr x30 = 1620 units of work

Works get increased by 10 times

new work = 16200, hrs given 25days x 8 hrs = 200 hrs

16200/200 = 81 machines

KarishmaB · Answer

Yes, it is correct. You can put the question in terms of units of work.

GMAT695 · Answer

M 1 D 1 H 1  / W 1 = M 2 D 2 H 2  / W 2  
  A= number of men.
6 x 30 x 9 /1 = A x 25 x 8/ 10

A= 81.

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

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