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Question of the Week- 21 (A group of 30 men and 10 women working ....)

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Question of the Week- 21 (A group of 30 men and 10 women working ....)  [#permalink]

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New post 02 Nov 2018, 02:54
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e-GMAT Question of the Week #21

A group of 40 workers working together have to complete a piece of work in 30 days. If all the workers work at a constant rate and after 20 days, it was found that only \(\frac{1}{4}^{th}\) of the work was completed, then how many more workers should be recruited so that the work gets completed on time?

    A. 32
    B. 100
    C. 200
    D. 240
    E. 280

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Re: Question of the Week- 21 (A group of 30 men and 10 women working ....)  [#permalink]

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New post 02 Nov 2018, 06:51
They finished 1/4 or 25% work in 20 days.
Therefore , 40 workers will take 20*4 = 80 days to finish the job from scratch.
20 days has already passed. To finish the job in 10 days , workers needed = 8 * 40 = 320.
Additional workers required = 320-40 = 280
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Re: Question of the Week- 21 (A group of 30 men and 10 women working ....)  [#permalink]

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New post 02 Nov 2018, 07:18
1
I've solved this differently.

40 workers, 20 days, 1/4
40 workers, 10 days, 1/2 * 1/4 = 1/8

Amount of work incomplete - 3/4

Therefore, if 40 workers complete 1/8th of the work in 10 days, we should have 240 (40*6) workers to complete 6*(1/8) work in 10 days.

Additional workers = 240 - the 40 who are already working = 200 I.e. (C)

Hope this helps.

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Re: Question of the Week- 21 (A group of 30 men and 10 women working ....)  [#permalink]

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New post 05 Nov 2018, 11:37
Hey Nikhilaery, can you explain how did you arrive at
Quote:
Therefore, if 40 workers complete 1/8th of the work in 10 days, we should have 240 (40*6) workers to complete 6*(1/8) work in 10 days.
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Question of the Week- 21 (A group of 30 men and 10 women working ....)  [#permalink]

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New post 05 Nov 2018, 17:17
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Hi Harsh,

Firstly, the key is "all the workers work at a constant rate".

I hope you understand how I arrived at 40 workers complete 1/8th piece of work in 10 days.

So knowing that 1/4th of work is already completed, we can infer that 3/4th is still pending. If I could arrive at an equation which could tell me how many workers and days will be required to finish 3/4th of pending work, that would suffice my requirement.

40 workers in 10 days complete 1/8th piece of work.

So, let's say, if in the same period I have to double the work being done in 10 days or same time, I'll simply double the number of workers working at a constant rate.

I'll thus say
40 workers x 2 in 10 days will do double the work they do I.e. 2 x 1/8th piece of work

Now, we know that what's pending is 3/4th. And 6 x (1/8) will give us (3/4)

So, if you want to finish the pending work in 10 days, you'll have to increase the workers.

Hence, 40 workers x 6 in 10 days will complete 3/4th of pending work.

Hope this helps.

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Re: Question of the Week- 21 (A group of 30 men and 10 women working ....)  [#permalink]

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New post 05 Nov 2018, 20:32
1
EgmatQuantExpert wrote:

A group of 40 workers working together have to complete a piece of work in 30 days. If all the workers work at a constant rate and after 20 days, it was found that only \(\frac{1}{4}^{th}\) of the work was completed, then how many more workers should be recruited so that the work gets completed on time?

    A. 32
    B. 100
    C. 200
    D. 240
    E. 280


Hi,

If all the workers work at a constant rate and after 20 days, it was found that only \(\frac{1}{4}^{th}\) of the work was completed

=> \(\frac{1}{4}\) of the work = 20*40 workerdays = 800 workerdays.

Remaining work = \(\frac{3}{4}\) of the work = 3* 800 = 2400 workerdays.

Remaining work has to be completed in 10 days. => Number of workers required = \(\frac{2400}{10}\) = 240 workers.

40 workers are already working, hence the additional number of required workers = 240 - 40 = 200 workers. Answer: (C).

Thanks.
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Re: Question of the Week- 21 (A group of 30 men and 10 women working ....)  [#permalink]

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New post 06 Nov 2018, 04:28
Hi Nikhilaery

Thanks this helps

Quote:
Hi Harsh,

Firstly, the key is "all the workers work at a constant rate".

I hope you understand how I arrived at 40 workers complete 1/8th piece of work in 10 days.

So knowing that 1/4th of work is already completed, we can infer that 3/4th is still pending. If I could arrive at an equation which could tell me how many workers and days will be required to finish 3/4th of pending work, that would suffice my requirement.

40 workers in 10 days complete 1/8th piece of work.

So, let's say, if in the same period I have to double the work being done in 10 days or same time, I'll simply double the number of workers working at a constant rate.

I'll thus say
40 workers x 2 in 10 days will do double the work they do I.e. 2 x 1/8th piece of work

Now, we know that what's pending is 3/4th. And 6 x (1/8) will give us (3/4)

So, if you want to finish the pending work in 10 days, you'll have to increase the workers.

Hence, 40 workers x 6 in 10 days will complete 3/4th of pending work.

Hope this helps.
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Re: Question of the Week- 21 (A group of 30 men and 10 women working ....)  [#permalink]

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New post 11 Nov 2018, 18:40
Given:
    • Initial number of workers = 40
    • The work must be completed in 30 days
    • After, 20 days, only \(\frac{1}{4}^{th}\) of the work was completed
    • All the workers work at a constant rate

To find:
    • The number of new workers to be recruited, so that the work gets completed on time

Approach and Working:
    • If 40 workers can complete \(\frac{1}{4}^{th}\) of the work in 20 days, they can finish the work in 20 * 4 = 80 days.
      o Implies, total work = 40 * 80 ………… (1)

    • Now, let us assume that the number of new workers = x
    • Thus, 40 + x workers must finish the rest \(\frac{3}{4}^{th}\) of the work in remaining 10 days
      o Implies, total work = \((40 + x) * 10 * \frac{4}{3}\) …………. (2)

    Equating (1) and (2), we get,
    • \(40 * 80 = (\frac{40}{3}) * (40 + x)\)
    • Thus, x = 240 – 40 = 200

Hence the correct answer is Option C.

Answer: C
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Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
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Re: Question of the Week- 21 (A group of 30 men and 10 women working ....) &nbs [#permalink] 11 Nov 2018, 18:40
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