A, B, and C were to be paid in proportion to the part of work they did while working on the same piece of work. A and B individually can finish the piece of work in 12 days and 15 days respectively. They worked together for five days and then C completed the remaining work all alone. If $720 was the net sum to be paid for the entire work, what was the average daily wage of B?
(A) $144
(B) $90
(C) $60
(D) $54
(E) $48
work all alone
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Per day work done by A & B = (1/12) + (1/15) = 9/60. After 5 days amount of work done = (9/60) * 5 = 3/4 th.sanju09 wrote:A, B, and C were to be paid in proportion to the part of work they did while working on the same piece of work. A and B individually can finish the piece of work in 12 days and 15 days respectively. They worked together for five days and then C completed the remaining work all alone. If $720 was the net sum to be paid for the entire work, what was the average daily wage of B?
(A) $144
(B) $90
(C) $60
(D) $54
(E) $48
so together, they will receive 3/4th of $720 i.e $540. Also, ratio of work done by B and A = 5/4 (15/12)
Or B gets 5/9th of the amount = (4/9) * 540 = $ 4 * 60
So, avg daily wage = [spoiler]$ (4 * 60) / 5 = $ 48. IMO E[/spoiler]
*Calculation mistake
Last edited by harshavardhanc on Tue Mar 23, 2010 3:03 am, edited 1 time in total.
Regards,
Harsha
Harsha
Great Question!
Here we go :
A does 1/12
B does 1/15
In 5 days they did together 5*( 1/12 + 1/ 15) = 3/4
Thus A+B have received 720* 3/4 = 540 ( amount paid for 5 day's work )
Now we need to determine what proportion of work has B done :
5/15 : 3/4 = 4/9 now e know that B has received 4/9*540= 240 for 5 days or 240/5 = 48 average
[spoiler]thus E ![/spoiler]
Here we go :
A does 1/12
B does 1/15
In 5 days they did together 5*( 1/12 + 1/ 15) = 3/4
Thus A+B have received 720* 3/4 = 540 ( amount paid for 5 day's work )
Now we need to determine what proportion of work has B done :
5/15 : 3/4 = 4/9 now e know that B has received 4/9*540= 240 for 5 days or 240/5 = 48 average
[spoiler]thus E ![/spoiler]
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Very economical approachGiorgio wrote:Great Question!
Here we go :
A does 1/12
B does 1/15
In 5 days they did together 5*( 1/12 + 1/ 15) = 3/4 = 9/12Thus A+B have received 720* 3/4 = 540 ( amount paid for 5 day's work ) = Now we need to determine what proportion of work has B done :
5/15 : 3/4 = 4/9 now e know that B has received 4/9*540= 240 for 5 days or 240/5 = 48 average [spoiler]thus E ![/spoiler]
the bold part - we know the relative time A and B take to do the work 12 : 15 so their ratio of work done will be 15 : 12 i.e payment received will be in the ratio 5 : 4
Infact if you do not breakdown any calc it kind of falls into palce at the end
B's share is = 4/9*9/12 * 720
Also for 5 days they get 540 so for one day A and B gets 108 since B gets less than A so option E
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Hi,
I have also come up with ans E
However i used a different approach.
B's rate is 1/15, and B worked for 5 days so he as done 5/15 or 1/3 of the job.
So B should get (1/3) of 720 which is 240. Considering that the question is asking for his average daily wage, then its 240/5, which is 48
I have also come up with ans E
However i used a different approach.
B's rate is 1/15, and B worked for 5 days so he as done 5/15 or 1/3 of the job.
So B should get (1/3) of 720 which is 240. Considering that the question is asking for his average daily wage, then its 240/5, which is 48
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sooooooper!! .... that's even shorter!!!! thanks mate!November Rain wrote:Hi,
I have also come up with ans E
However i used a different approach.
B's rate is 1/15, and B worked for 5 days so he as done 5/15 or 1/3 of the job.
So B should get (1/3) of 720 which is 240. Considering that the question is asking for his average daily wage, then its 240/5, which is 48
Regards,
Harsha
Harsha
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Yep, a lot of the problem is filler, all you really need to realize is what the problem is asking. This is definitely the fastest way to do it.November Rain wrote:Hi,
I have also come up with ans E
However i used a different approach.
B's rate is 1/15, and B worked for 5 days so he as done 5/15 or 1/3 of the job.
So B should get (1/3) of 720 which is 240. Considering that the question is asking for his average daily wage, then its 240/5, which is 48
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Awesome...how we can not pay attention to all the info and just with whats been asked!November Rain wrote:Hi,
I have also come up with ans E
However i used a different approach.
B's rate is 1/15, and B worked for 5 days so he as done 5/15 or 1/3 of the job.
So B should get (1/3) of 720 which is 240. Considering that the question is asking for his average daily wage, then its 240/5, which is 48
Thx!
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Let the total work be 60sanju09 wrote:A, B, and C were to be paid in proportion to the part of work they did while working on the same piece of work. A and B individually can finish the piece of work in 12 days and 15 days respectively. They worked together for five days and then C completed the remaining work all alone. If $720 was the net sum to be paid for the entire work, what was the average daily wage of B?
(A) $144
(B) $90
(C) $60
(D) $54
(E) $48
A can do 5 units of work in a day
B can do 4 units of work in a day
Hence in 5 days A does 25 units
B does 20 units
Work left is 60 - ( 20 +25 ) = 15 units.
Thus C does 15 units.
Ratio of work done by B is 20/60 => 1/3rd of the total work so he will receive 1/3 rd of $240
Average daily wage of B is Earning / Number of days B worked = > 240 / 5 = 48 .
Abhishek
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Let job = 60 units.sanju09 wrote:A, B, and C were to be paid in proportion to the part of work they did while working on the same piece of work. A and B individually can finish the piece of work in 12 days and 15 days respectively. They worked together for five days and then C completed the remaining work all alone. If $720 was the net sum to be paid for the entire work, what was the average daily wage of B?
(A) $144
(B) $90
(C) $60
(D) $54
(E) $48
Rate for B = w/t = 60/15 = 4 units per day.
Work produced by B in 5 days = r*t = 4*5 = 20 units.
Since B produces 20 of the 60 units -- 1/3 of the job -- B receives 1/3 of the total pay:
(1/3)(720) = 240.
Since B works for 5 days, the average daily pay for B = 240/5 = 48.
The correct answer is E.
Last edited by GMATGuruNY on Tue Jan 13, 2015 2:48 am, edited 1 time in total.
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A and C are decoys - totally beside the point to solve this question.
B can do the work in 15 days. He worked 5 days = 1/3 of the time so he did 1/3 of the work and gets 1/3 of the money.
$720/3 = $240
Average = $240/5 = $48
B can do the work in 15 days. He worked 5 days = 1/3 of the time so he did 1/3 of the work and gets 1/3 of the money.
$720/3 = $240
Average = $240/5 = $48
If you found one of my answers useful, hit the shiny Thanks button! : )
I considered this problem this way :
Q said NET amount paid is 720 $. So if they are asking only for B, then if B works all alone for 15 days he will receive 720 $. So daily avg rate for B will be 720/15 = 48 $.
Mitch,
please correct in case any assumption I'm missing.
Q said NET amount paid is 720 $. So if they are asking only for B, then if B works all alone for 15 days he will receive 720 $. So daily avg rate for B will be 720/15 = 48 $.
Mitch,
please correct in case any assumption I'm missing.
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In 5 days A and B together finish 5(1/12+1/15) = 45/60
Remaining = 15/60 done by C
Ratio = 5/12:5/15:15/60 = 25:20:15
B salary total = 12*20
Avg daily wage = 12*20/5 = 48
Remaining = 15/60 done by C
Ratio = 5/12:5/15:15/60 = 25:20:15
B salary total = 12*20
Avg daily wage = 12*20/5 = 48
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