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All employees of Company A and Company B work together on some project

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All employees of Company A and Company B work together on some project  [#permalink]

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New post Updated on: 29 Oct 2018, 22:32
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Question Stats:

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All employees of Company A and Company B work together on some project. The ratio of number of employees in company A and company B is 5: 6, and each employee of company A can do the work 3 times faster than each employee of company B. What fraction of the project is done by the employees of company B?

    A. 5/18
    B. 2/7
    C. 2/5
    D. 5/7
    E. 18/23

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Originally posted by EgmatQuantExpert on 27 Sep 2018, 02:43.
Last edited by EgmatQuantExpert on 29 Oct 2018, 22:32, edited 1 time in total.
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Re: All employees of Company A and Company B work together on some project  [#permalink]

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New post 27 Sep 2018, 07:09
1
Ratio of A:B = 5:6 ; A works 3x faster than B
5x3 : 6 = 15 : 6
Part of the work B that completes = 6/21 = 2/7
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Re: All employees of Company A and Company B work together on some project  [#permalink]

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New post 27 Sep 2018, 07:25
1
EgmatQuantExpert wrote:
All employees of Company A and Company B work together on some project. The ratio of number of employees in company A and company B is 5: 6, and each employee of company A can do the work 3 times faster than each employee of company B. What fraction of the project is done by the employees of company B?

    A. 5/18
    B. 2/7
    C. 2/5
    D. 5/7
    E. 18/23

To read all our articles:Must read articles to reach Q51

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A/B = 5/6
we are given
when A does 1 unit of work
B does 1/3 units of work
so,
5 employees of A will do 5 units of work.
6 employees of B will do 6*\(\frac{1}{3}\) = 2 units of work

fraction of project done by employees of B = \(\frac{B}{A+B}\) =\(\frac{2}{7}\)
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Re: All employees of Company A and Company B work together on some project  [#permalink]

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New post 03 Oct 2018, 04:12
1

Solution


Given:
    • All the employees of Company A and B work on the same project
    • The ratio of number of employees in company A to company B = 5: 6
    • Each employee of company A can do the work 3 times faster, when compared to each employee of company B

To find:
    • What fraction of the project is done by employees of company B

Approach and Working:
    • Let us assume that the number of employees in company A = 5x
      o Implies, the number of employees in company B = 6x

    • Now, let us assume that each employee of company A can do 'y' amount of work in one day
      o Implies, each employee of company B can do '3y' amount of work in one day

    • So, \(\frac{Work done by all the employees of company A}{Work done by all the employees of company B}\) = \(\frac{(5x * 3y)}{(6x * y)} = \frac{15}{6} = \frac{5}{2}\)

Therefore, the fraction of work done by employees of company B = \(\frac{2}{(2 + 5)} = \frac{2}{7}\)

Hence, the correct answer is Option B.

Answer: B

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Re: All employees of Company A and Company B work together on some project  [#permalink]

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New post 15 Nov 2018, 07:13
Hi egmat

Can we use your LCM method in this type of problem ? I wasnt able to solve through LCM and ended up choosing 2/5.
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All employees of Company A and Company B work together on some project  [#permalink]

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New post 15 Nov 2018, 09:18
hero_with_1000_faces wrote:
Hi egmat

Can we use your LCM method in this type of problem ? I wasnt able to solve through LCM and ended up choosing 2/5.


Hi,

Could you please show us, how you approached at solving this question, so that we can understand it in a better way :)

Regards,
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All employees of Company A and Company B work together on some project  [#permalink]

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New post 15 Nov 2018, 09:34
EgmatQuantExpert wrote:
All employees of Company A and Company B work together on some project. The ratio of number of employees in company A and company B is 5: 6, and each employee of company A can do the work 3 times faster than each employee of company B. What fraction of the project is done by the employees of company B?

    A. 5/18
    B. 2/7
    C. 2/5
    D. 5/7
    E. 18/23

To read all our articles:Must read articles to reach Q51

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Ratio of number of employees:
\(A:B = 5:6\)
Since A works 3 times faster than B
Then ratio of the work being done:
\(Wa:Wb = 5*3 : 6 = 15 : 6\)

Hence total work = 6 + 15 = 21
Ratio of work done by B to the total work:
Wb:Wt = \(\frac{6}{21} = \frac{2}{7}\)
Hence B is the correct answer.
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Re: All employees of Company A and Company B work together on some project  [#permalink]

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New post 16 Nov 2018, 17:25
EgmatQuantExpert wrote:
hero_with_1000_faces wrote:
Hi egmat

Can we use your LCM method in this type of problem ? I wasnt able to solve through LCM and ended up choosing 2/5.


Hi,

Could you please show us, how you approached at solving this question, so that we can understand it in a better way :)

Regards,



Hi,

I am sorry, I discarded the worksheet, before I saw your reply. But I tried solving this again and I ended up with correct answer although it logically doesnt make sense to me, if you could review that would be great:



So, A : B, 5x : 6x

As the employees for A are three times more efficient, that means one employee of "A" can work as much as three employees of "B".
So 5 * 3 = 15, so the ratio 15x : 6x; so now taking the LCM of 15 and 6 we get 30, from here on my answer doesn't logically make sense to me.

for A 30/15 = 2

for B 30/6 = 5

so total work is "7" and therefore 2/7. after solving I realized the question is asking for the part of work done by "B".
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Re: All employees of Company A and Company B work together on some project  [#permalink]

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New post 16 Nov 2018, 22:16
EgmatQuantExpert wrote:
All employees of Company A and Company B work together on some project. The ratio of number of employees in company A and company B is 5: 6, and each employee of company A can do the work 3 times faster than each employee of company B. What fraction of the project is done by the employees of company B?

    A. 5/18
    B. 2/7
    C. 2/5
    D. 5/7
    E. 18/23



Ratio of employees of \(\frac{Company A}{Company B}\) = \(\frac{5x}{6x}\)

Say rate of Company B's employee = R,

Then rate of Company A's employee =3R

As both worked for equal time, time for both = T

We know:

Employees x Rate x Time = Work

For company A 5x * 3R * T = 15xRT

For company B 6x * R * T = 6xRT

Total work = \(15xRT + 6xRT = 21xRT\)

Work Done by \(B = 6xRT\)

Required fraction = \(\frac{6xRT}{21xRT}\) = \(\frac{2}{7}\)
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Re: All employees of Company A and Company B work together on some project &nbs [#permalink] 16 Nov 2018, 22:16
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