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

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A, B and C work on a task. To complete the task alone, B [#permalink] New post   26 Jun 2014, 21:03
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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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Re: A, B and C work on a task. To complete the task alone, B [#permalink] New post   27 Jun 2014, 02:07
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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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A, B and C work on a task. To complete the task alone, B [#permalink] New post   29 Oct 2014, 12:46
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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 \(\frac{1/4}{1+1/4+1/9} = \frac{9}{49}\).

Answer: C
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Re: A, B and C work on a task. To complete the task alone, B [#permalink] New post   30 Oct 2014, 20:56
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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

Hence Answer C.
--------------------------------

Kudos please, if this post helps.
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Re: A, B and C work on a task. To complete the task alone, B [#permalink] New post   23 Feb 2018, 20:07
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

Hence Answer C.
--------------------------------

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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Re: A, B and C work on a task. To complete the task alone, B [#permalink] New post   23 Feb 2018, 21:23
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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

Hence Answer C.
--------------------------------

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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A, B and C work on a task. To complete the task alone, B [#permalink] New post   Updated on: 05 Jul 2020, 22:45
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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

:cool: :cool: :cool: :cool:

Originally posted by HouseStark on 30 Jun 2020, 01:03.
Last edited by HouseStark on 05 Jul 2020, 22:45, edited 2 times in total.
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Re: A, B and C work on a task. To complete the task alone, B [#permalink] New post   05 Jul 2020, 10:20
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

:cool: :cool: :cool: :cool:
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Re: A, B and C work on a task. To complete the task alone, B [#permalink] New post   05 Jul 2020, 22:49
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.
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Re: A, B and C work on a task. To complete the task alone, B [#permalink] New post   20 Oct 2023, 23:05
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