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

Question

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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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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CounterSniper · Accepted Answer

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}

pandeyashwin · Answer

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

EgmatQuantExpert · Answer

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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hero_with_1000_faces · Answer

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.

EgmatQuantExpert · Answer

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

Regards,

eabhgoy · Answer

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.

hero_with_1000_faces · Answer

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".

AkshdeepS · Answer

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}

Apeksha2101 · Answer

The question as A works 3 times faster than B, so it should be 3x + x = 4x , if the statement was 3 times as faster as B , then it should be x. Please explain

PSKhore · Answer

Let's assume that there are 5 employees in company A and 6 employees in company B.

When 1 employee from company B does 1 unit of work, then 1 employee of company A does 3 units of work.

Work done by employees from company B = 6*1 = 6 units

Work done by employees from company A = 5*3 = 15 units units
 
Proportion of work done by company B = 6/(6+15) = 6/21
 =3/7

Advait01 · Answer

The solution seems really easy, i wasted my time doing actual calculation

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

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