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Director  S
Joined: 17 Dec 2012
Posts: 636
Location: India

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Difficulty:   95% (hard)

Question Stats: 50% (03:20) correct 50% (03:05) wrong based on 121 sessions

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A, B and C work on a task. To complete the task alone, B takes twice the time that A would take to complete the task alone and 2/3rd the time that C would take to complete the task alone. If B actually worked for half the number of days that A worked and 3/2 times the number of days that C worked, what proportion of the total work was completed by B?

A. 1/3
B. 2/9
C. 9/49
D. 7/19
E. 1/6

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Srinivasan Vaidyaraman
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Holistic and Holy Approach
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SravnaTestPrep wrote:
A, B and C work on a task. To complete the task alone, B takes twice the time that A would take to complete the task alone and 2/3rd the time that C would take to complete the task alone. If B actually worked for half the number of days that A worked and 3/2 times the number of days that C worked, what proportion of the total work was completed by B?

A. 1/3
B. 2/9
C. 9/49
D. 7/19
E. 1/6

efficiency of A in doing the work = x
efficiency of B in doing the work = x/2
efficiency of C in doing the work = x/3

now suppose A work for 6 days, then b will work for 3 days and C will work for 2 days

proportion of work completed by B = 3(x/2) / (6x+3(x/2)+2(x/3)
= 9/49
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Joined: 23 May 2013
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Concentration: Technology, Healthcare
GMAT 1: 760 Q49 V45 GPA: 3.5

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SravnaTestPrep wrote:
A, B and C work on a task. To complete the task alone, B takes twice the time that A would take to complete the task alone and 2/3rd the time that C would take to complete the task alone. If B actually worked for half the number of days that A worked and 3/2 times the number of days that C worked, what proportion of the total work was completed by B?

A. 1/3
B. 2/9
C. 9/49
D. 7/19
E. 1/6

This is a variable question, so we can just assign arbitrary values to simplify the problem greatly.

To complete the task alone, B takes twice the time that A would take to complete the task alone and 2/3rd the time that C would take to complete the task alone. If it takes 1 day for A to do the project, then it takes 2 days for B and 3 days for C.

If B actually worked for half the number of days that A worked and 3/2 times the number of days that C worked, what proportion of the total work was completed by B?

Let's say A worked 1 day. Then A completed 1 project. B worked for 1/2 a day, and since it takes him 2 days, he completed $$\frac{1/2}{2} = \frac{1}{4}$$ of a project. C then worked for 1/3 of a day, and completed $$\frac{1/3}{3} = \frac{1}{9}$$ of a project.

Then to find the proportion, we take $$\frac{1/4}{1+1/4+1/9} = \frac{9}{49}$$.

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SravnaTestPrep wrote:
A, B and C work on a task. To complete the task alone, B takes twice the time that A would take to complete the task alone and 2/3rd the time that C would take to complete the task alone. If B actually worked for half the number of days that A worked and 3/2 times the number of days that C worked, what proportion of the total work was completed by B?

A. 1/3
B. 2/9
C. 9/49
D. 7/19
E. 1/6

The first thing to notice is that A is faster than B and B is faster than C.

Since work is proportional to time, in 1 day lets say if A does 2 works, B does 1 work and C does 2/3rd of a work.

If A works for 2 days, B works for 1 day and C works for only 2/3 of the day.

Therefore total work done = (2*2) + (1*1) + (2/3*2/3) = 49/9

Proportion of work done by B = (1*1) / (49/9) = 9/49

--------------------------------

Kudos please, if this post helps.
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Vetrik wrote:
SravnaTestPrep wrote:
A, B and C work on a task. To complete the task alone, B takes twice the time that A would take to complete the task alone and 2/3rd the time that C would take to complete the task alone. If B actually worked for half the number of days that A worked and 3/2 times the number of days that C worked, what proportion of the total work was completed by B?

A. 1/3
B. 2/9
C. 9/49
D. 7/19
E. 1/6

The first thing to notice is that A is faster than B and B is faster than C.

Since work is proportional to time, in 1 day lets say if A does 2 works, B does 1 work and C does 2/3rd of a work.

If A works for 2 days, B works for 1 day and C works for only 2/3 of the day.

Therefore total work done = (2*2) + (1*1) + (2/3*2/3) = 49/9

Proportion of work done by B = (1*1) / (49/9) = 9/49

--------------------------------

Kudos please, if this post helps.

How did you arrive at ...C does 2/3 of the work??? I did not understand ...B works for 3/2 times the number of days C worked???
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Kezia9 wrote:
Vetrik wrote:
SravnaTestPrep wrote:
A, B and C work on a task. To complete the task alone, B takes twice the time that A would take to complete the task alone and 2/3rd the time that C would take to complete the task alone. If B actually worked for half the number of days that A worked and 3/2 times the number of days that C worked, what proportion of the total work was completed by B?

A. 1/3
B. 2/9
C. 9/49
D. 7/19
E. 1/6

The first thing to notice is that A is faster than B and B is faster than C.

Since work is proportional to time, in 1 day lets say if A does 2 works, B does 1 work and C does 2/3rd of a work.

If A works for 2 days, B works for 1 day and C works for only 2/3 of the day.

Therefore total work done = (2*2) + (1*1) + (2/3*2/3) = 49/9

Proportion of work done by B = (1*1) / (49/9) = 9/49

--------------------------------

Kudos please, if this post helps.

How did you arrive at ...C does 2/3 of the work??? I did not understand ...B works for 3/2 times the number of days C worked???

We can use ratios to understand it better-
Given that B worked half the number of days that A worked,implies: B= (1/2)*A
Or, A/B = 2/1 (Here it means that when A works for 2 days,B works for a day).

Now, relating B and C: B works 3/2 times C.
Or, B= (3/2)*C
B/C = 3/2.
This can be rewritten as : B/C = 1/(2/3) {In other words, when B works for a day, C works for 2/3 day}

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Manager  S
Status: BELIEVE IN YOURSELF
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SravnaTestPrep wrote:
A, B and C work on a task. To complete the task alone, B takes twice the time that A would take to complete the task alone and 2/3rd the time that C would take to complete the task alone. If B actually worked for half the number of days that A worked and 3/2 times the number of days that C worked, what proportion of the total work was completed by B?

A. 1/3
B. 2/9
C. 9/49
D. 7/19
E. 1/6

Quote:
To complete the task alone, B takes twice the time that A would take to complete the task alone and 2/3rd the time that C would take to complete the task alone

A=A
B=2A
B=$$\frac{2}{3}$$C

Put the value of B here, so that we can get everything in term A
so, C=3A

Quote:
B actually worked for half the number of days that A worked and 3/2 times the number of days that C worked

A=x
B=$$\frac{1}{2}$$x
B=$$\frac{3}{2}$$C

In this also we put value of B so that we can get everything in term of x
C=$$\frac{1}{3}$$x

Now for suppose the x=6.
A=6
B=3
C=2

Let,total work =1

work is done by A, $$\frac{1}{A}$$=$$\frac{W(A)}{6}$$= W(A)=$$\frac{6}{A}$$

work is done by B, $$\frac{1}{2A}$$=$$\frac{W(B)}{3}$$= W(B)=$$\frac{3}{2A}$$

work is done by C, $$\frac{1}{3A}$$=$$\frac{W(C)}{2}$$= W(C)=$$\frac{2}{3A}$$

now the proportion of the total work was completed by B

$$\frac{(3|2A)}{(6/A)+(3/2A)+(2/3A)}$$
=$$\frac{9A}{49A}$$
=9/49

IMO C    Originally posted by HouseStark on 30 Jun 2020, 00:03.
Last edited by HouseStark on 05 Jul 2020, 21:45, edited 2 times in total.
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HouseStark wrote:
SravnaTestPrep wrote:
A, B and C work on a task. To complete the task alone, B takes twice the time that A would take to complete the task alone and 2/3rd the time that C would take to complete the task alone. If B actually worked for half the number of days that A worked and 3/2 times the number of days that C worked, what proportion of the total work was completed by B?

A. 1/3
B. 2/9
C. 9/49
D. 7/19
E. 1/6

Quote:
To complete the task alone, B takes twice the time that A would take to complete the task alone and 2/3rd the time that C would take to complete the task alone

A=A
B=2A
B=$$\frac{2}{3}$$C

Can you check and confirm: Both your assumptions are time variables: A=A is Time; A=x is also time. You have then multiplied timextime to calculate work!
Am i missing something here?

Put the value of B here, so that we can get everything in term A
so, C=3A

Quote:
B actually worked for half the number of days that A worked and 3/2 times the number of days that C worked

A=x
B=$$\frac{1}{2}$$x
B=$$\frac{3}{2}$$C

In this also we put value of B so that we can get everything in term of x
C=$$\frac{1}{3}$$x

Now for suppose the x=6.
A=6
B=3
C=2

now the proportion of the total work was completed by B

$$\frac{3*3A}{6*6A+3*3A+2*2A}$$
=$$\frac{9A}{49A}$$
=9/49

IMO C    Manager  S
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Quote:
Can you check and confirm: Both your assumptions are time variables: A=A is Time; A=x is also time. You have then multiplied timextime to calculate work!
Am I missing something here?

yes, I have done it wrong on the last part calculating the proportion of the total work completed by B.

Thanks, Rachit4126 now, I have corrected it. Re: A, B and C work on a task. To complete the task alone, B   [#permalink] 05 Jul 2020, 21:49

# A, B and C work on a task. To complete the task alone, B   