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10 men take 30 minutes to wrap 100 articles. How long will it take 40

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10 men take 30 minutes to wrap 100 articles. How long will it take 40  [#permalink]

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New post 26 Oct 2017, 21:32
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

61% (01:41) correct 39% (01:43) wrong based on 134 sessions

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10 men take 30 minutes to wrap 100 articles. How long will it take 40 men to wrap 200 articles if the new team is half as efficient?

A. 7.5 minutes
B. 15 minutes
C. 30 minutes
D. 60 minutes
E. 120 minutes

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Re: 10 men take 30 minutes to wrap 100 articles. How long will it take 40  [#permalink]

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New post 26 Oct 2017, 23:22
1
nkmungila wrote:
10 men take 30 minutes to wrap 100 articles. How long will it take 40 men to wrap 200 articles if the new team is half as efficient?

A. 7.5 minutes
B. 15 minutes
C. 30 minutes
D. 60 minutes
E. 120 minutes


If 10 men take 30 minutes to wrap 100 articles,
we can say that 10*30 = 300 men minutes were spent to wrap 100 articles.
Since, we have to wrap 200 articles and have 40 men for the job,
the time taken to wrap 200 articles must be twice the time(600 men minutes)
Hence as is, the 40 men take 15 minutes to do the job!

Since the men are half as efficient, they must take 15*2 or 30 minutes to do the wrapping(Option C)
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Re: 10 men take 30 minutes to wrap 100 articles. How long will it take 40  [#permalink]

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New post 26 Oct 2017, 23:44
1
If 10 guys take 30 minutes to wrap 100 articles.
Then 40 fully efficient men will take (30mins*2)/(4) = 15mins to wrap 200 articles.
But as they are half only as efficient they will take double time, hence 15*2= 30 mins.






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Re: 10 men take 30 minutes to wrap 100 articles. How long will it take 40  [#permalink]

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New post 27 Oct 2017, 01:14
1
1
M - Number of men
D - Number of days
H - Number of hours
E - Efficiency
W - Work done

Using this - M*D*H*E/W we get

10*D*0.5*E*1/100 = 40*D*H*E/2*1/200

Find H

Option C


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10 men take 30 minutes to wrap 100 articles. How long will it take 40  [#permalink]

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New post 27 Oct 2017, 10:35
2
2
nkmungila wrote:
10 men take 30 minutes to wrap 100 articles. How long will it take 40 men to wrap 200 articles if the new team is half as efficient?

A. 7.5 minutes
B. 15 minutes
C. 30 minutes
D. 60 minutes
E. 120 minutes

Attachment:
WRTvar.png
WRTvar.png [ 24.34 KiB | Viewed 1116 times ]

One quick way (well under a minute): Modify the standard R*T= W formula. Add Number of workers (or machines, etc.) to LHS

Modified RTW formula: (# of workers) * R * T = W

Use the first scenario to find unknowns in second scenario.
Here, find Group 1's individual rate to find rate and time for Group 2.

1) Individual worker rate for Group 1?

W = (# of workers) * R * T

\(100 = 10 * R * 30\)

\(\frac{100}{(10 * 30)} = R\)

\(R = \frac{100}{300}\)
= \(\frac{1}{3}\)

2) Group 2 individual rate?

Individual worker rate in Group 1 = \(\frac{1}{3}\)

Group 2 workers are half as efficient:

\(\frac{(\frac{1}{3})}{2} = (\frac{1}{3} * \frac{1}{2} ) =\)

\(\frac{1}{6}\)= individ rate of Group 2

3) How long will it take 40 men [working at Group 2's individual rate] to wrap 200 articles?

W = (# of workers) * R * TIME

\(200 = 40 * \frac{1}{6}* TIME\)

\(TIME = \frac{200}{(40 * \frac{1}{6})} = \frac{200}{(\frac{40}{6})}\)

\(TIME = 200 * (\frac{6}{40}) = (5 *6) =\)


30 minutes

Answer C
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Re: 10 men take 30 minutes to wrap 100 articles. How long will it take 40  [#permalink]

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New post 27 Oct 2017, 19:56
By using this MDHE/W
M-man
D -days
H-hrs
E -efficiency
W-work
And we get new time-30 min
Ans-Option C


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Re: 10 men take 30 minutes to wrap 100 articles. How long will it take 40  [#permalink]

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New post 30 Oct 2017, 13:09
nkmungila wrote:
10 men take 30 minutes to wrap 100 articles. How long will it take 40 men to wrap 200 articles if the new team is half as efficient?

A. 7.5 minutes
B. 15 minutes
C. 30 minutes
D. 60 minutes
E. 120 minutes


The rate of 10 men is 100/30 = 10/3. Let’s say the 40 men are just as efficient as the 10 men. Using the following proportion, we can determine the rate of the 40 men:

10/(10/3) = 40/n

30/10 = 40/n

3 = 40/n

3n = 40

n = 40/3

Thus, working just as efficiently as the 10 men, the 40 men can wrap 200 articles in 200/(40/3) = 600/40 = 15 minutes. Working half as efficiently, they would take 30 minutes.

Answer: C
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Re: 10 men take 30 minutes to wrap 100 articles. How long will it take 40  [#permalink]

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New post 09 Nov 2017, 10:02
1
10 men will wrap 100 articles in 30 minutes.
Half as efficient = double the time.

The same 10 men will wrap 100 articles in 60 mins or 1 hour.
The same 10 men will wrap 200 articles in 2 hours.
Hence, if you want 40 men to wrap the same 200 articles, we must divide the time by 4.

2/4 = 1/2 hour or 30 minutes. Answer is C.
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Re: 10 men take 30 minutes to wrap 100 articles. How long will it take 40 &nbs [#permalink] 09 Nov 2017, 10:02
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