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A, B and C work on a task. To complete the task alone, B
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26 Jun 2014, 20:03
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Difficulty:
95% (hard)
Question Stats:
47% (03:27) correct 53% (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?
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27 Jun 2014, 01:07
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
A, B and C work on a task. To complete the task alone, B
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29 Oct 2014, 11:46
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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 \(\frac{1/4}{1+1/4+1/9} = \frac{9}{49}\).
Re: A, B and C work on a task. To complete the task alone, B
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30 Oct 2014, 19:56
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
Re: A, B and C work on a task. To complete the task alone, B
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23 Feb 2018, 19:07
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???
Re: A, B and C work on a task. To complete the task alone, B
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23 Feb 2018, 20:23
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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47% (03:27) correct 
