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work all alone

by sanju09 » Tue Mar 23, 2010 2:22 am
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
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by harshavardhanc » Tue Mar 23, 2010 2:35 am
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
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.

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.
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by Giorgio » Tue Mar 23, 2010 2:40 am
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]
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by kstv » Tue Mar 23, 2010 7:47 am
Giorgio 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]
Very economical approach
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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by November Rain » Tue Mar 23, 2010 8:51 am
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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by kstv » Tue Mar 23, 2010 9:00 am
Knew I was missing something. The best approach.

We still can find a way
'Cause nothin' lasts forever
Even cold November rain
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by harshavardhanc » Tue Mar 23, 2010 9:00 am
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
sooooooper!! .... that's even shorter!!!! thanks mate!
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Harsha
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by chendawg » Mon Feb 21, 2011 5:22 pm
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
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.
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by anirudhbhalotia » Tue Apr 26, 2011 2:49 am
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
Awesome...how we can not pay attention to all the info and just with whats been asked!

Thx!
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by Abhishek009 » Tue Apr 26, 2011 4:25 am
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
Let the total work be 60

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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by GMATGuruNY » Tue Apr 26, 2011 6:10 am
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
Let job = 60 units.
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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by MM_Ed » Thu Oct 20, 2011 5:04 pm
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
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by DonPaw » Mon Nov 07, 2011 7:08 pm
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.
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by Sharma_Gaurav » Thu Apr 05, 2012 2:04 am
approach by November Rain is the fastest . option E - 48 is correct
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by ronnie1985 » Sat Apr 07, 2012 9:59 am
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
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