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working on the project

by sanju09 » Tue Apr 05, 2011 4:52 am
A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?
(A) 12
(B) 16
(C) 18
(D) 26
(E) 27
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by rohu27 » Tue Apr 05, 2011 5:07 am
let xbe the total number of days to complete the work.
rate of a=1/20
rate of B=1/30
so A leaves x-10 days before, in x-10 days A does x-10/20 th work.
in x days B does x/30th work.
the total shud be equal to 1 project.
so x-10/20+x/30=1.
on solving x=18
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by Anurag@Gurome » Tue Apr 05, 2011 5:07 am
sanju09 wrote:A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?
(A) 12
(B) 16
(C) 18
(D) 26
(E) 27
1 day work of A and B = 1/20 and 1/30 respectively.
Let the project is completed in N days.
Then B worked for all N days, and A worked for (N - 10) days.
This means A's contribution in the project = (N - 10)/20
B's contribution in the project = N/30
So, (N - 10)/20 + N/30 = 1 implies 3N - 30 + 2N = 60 or N = 18

The correct answer is C.
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by force5 » Tue Apr 05, 2011 5:22 am
Hi anurag... i have a different point of view please correct ...

A and B together can complete the work in 12 days. (1/20+1/30)
now A left 10 days before which means A and B virtually worked for only 2 days.
Work done in 2 days =1/12*2=1/6
remaining work = 5/6 is done alone by B
hence time taken by B should be 25days
total time taken 25+2= 27 days.

In the solution given you have mentioned B's contribution in the project is N/30 (please see that initially both worked together hence that cannot be B's contribution).

Please correct me if im wrong.
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by Anurag@Gurome » Tue Apr 05, 2011 5:29 am
force5 wrote:Hi anurag... i have a different point of view please correct ...

A and B together can complete the work in 12 days. (1/20+1/30)
now A left 10 days before which means A and B virtually worked for only 2 days.
Work done in 2 days =1/12*2=1/6
remaining work = 5/6 is done alone by B
hence time taken by B should be 25days
total time taken 25+2= 27 days.

In the solution given you have mentioned B's contribution in the project is N/30 (please see that initially both worked together hence that cannot be B's contribution).

Please correct me if im wrong.
First, how can we say that A and B together can complete the work in 12 days? (1/20 + 1/30) gives us 1 day work of (A + B) together. But we don't know for how long A and B worked together.
B's 1 day work = 1/30, so in N days, he can do N * (1/30) of the work, but please note that this does not include the work done by A.
A's 1 day work = 1/20, so in N-10 days, A can complete (N-10)/20 of the work.

Does that help?
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by force5 » Tue Apr 05, 2011 5:44 am
First, how can we say that A and B together can complete the work in 12 days? (1/20 + 1/30) gives us 1 day work of (A + B) together. But we don't know for how long A and B worked together.
B's 1 day work = 1/30, so in N days, he can do N * (1/30) of the work, but please note that this does not include the work done by A.
A's 1 day work = 1/20, so in N-10 days, A can complete (N-10)/20 of the work.

Does that help?
yes Anurag i understand what you are saying but how did we calculate the combined work that they both did?

I am considering work done to be 1
since both started working together their combined rate is 1/20+1/30= 1/12
which means they can complete the work together in 12 days......
now A leave 10 days before the work could be completed... which means effectively they worked together for 2 days...
in 2 days the amount of work they can do = 1/12*2= 1/6
since A quits B will have to complete the rest of the work..
remaining work is 5/6
B's rate = 1/30
hence time taken = 25 days..
total time 25+2= 27

Problem here is that we cannot calculate A contribution alone because they both started working together... if A worked for n-10 days they we cannot say A contribution is n-10/20 because actually both A and B worked together. Hence we will have to calculate combined rate. Thats why you are getting a smaller value.
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by GMATGuruNY » Tue Apr 05, 2011 10:16 am
sanju09 wrote:A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?
(A) 12
(B) 16
(C) 18
(D) 26
(E) 27
Plug in job = 60 units.
Rate for A alone = w/t = 60/20 = 3 units per day.
Rate for B alone = w/t = 60/30 = 2 units per day.
Combined rate for A+B together = 3+2 = 5 units per day.
Work completed by B alone in 10 days = r*t = 2*10 = 20 units.
Work to be completed by A+B = 60-20 = 40 units.
Time for A+B to complete 40 units = w/r = 40/5 = 8 days.
Total time = 10+8 = 18 days.

The correct answer is C.
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by Mike G » Tue Apr 05, 2011 10:22 am
force5
I used the same logic as you did and got the same answer.It seems essential to calculate combined rate for A and B,work performed by A and B and number of days they worked together.
Also, this method correspondes with that from Manhattan GMAT Word Translation Book.

Anurag,
can you please explain again.

Thanks
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by rohu27 » Tue Apr 05, 2011 10:31 am
Solving it using the combined rates approach.
let a and b worked together for x days, B works for 10 more days to finish off the owrk.
so in x days a and b 'together' do x/12 work (as 1 project in 12 days)
remaing work to be done by B in 10 days= 1-x/12=12-x/12
in 10 days B can do 1/3 work,
1/3=12-x/12 on simplification x=8
so the total no of days to complete the given work =8+10=18

force5,Mike,
using the combined rates method too the answer would be same.
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by force5 » Tue Apr 05, 2011 10:35 am
Plug in job = 60 units.
Rate for A alone = w/t = 60/20 = 3 units per day.
Rate for B alone = w/t = 60/30 = 2 units per day.
Combined rate for A+B together = 3+2 = 5 units per day.
Work completed by B alone in 10 days = r*t = 2*10 = 20 units.
Work to be completed by A+B = 60-20 = 40 units.
Time for A+B to complete 40 units = w/r = 40/5 = 8 days.
Total time = 10+8 = 18 days.
Mitch as per me this should be incorrect. it doesn't matter if you take work done as 1 or 60 or 10000. why r u calculating work done by B in 10 days??? how do you know the rest of the work was completed in 10 days??? the question says A quits 10 days before the project was completed( that was when both were working together) obviously now when A quit its going to take longer for B to complete....
Well i don't want to be difficult here for anyone. I described what i felt. Again you guys are the experts if you feel that way i don't want to argue further.....

Thanks guys...
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by GMATGuruNY » Tue Apr 05, 2011 10:42 am
force5 wrote:Hi anurag... i have a different point of view please correct ...

A and B together can complete the work in 12 days. (1/20+1/30)
now A left 10 days before which means A and B virtually worked for only 2 days.
A total time of 12 days presumes that A and B work together for the entire 12 days.
But since A leaves 10 days early -- leaving B to work alone for much of the project -- the total time will be much more than 12 days.
Thus, we can't say that 12-10 = 2 days is the time that A and B work together.

There is only one known time: for 10 days B works alone.

Thus, the problem could be rephrased:
B works alone on the project for 10 days.
Then A and B work together to finish the project.
What is the total number of days required to complete the project?
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by isanju » Tue Apr 05, 2011 10:08 pm
Let's solve it in reverse order:
B works alone for the last 10 days. So, he completes 1/3 (10/30) part of the complete work.
The remaining 2/3 part of work is completed by A and B together at a rate of (1/30 + 1/20) 1/12 per day. So, A & B together complete the work in 12 days
So, they work together for 8 days (12 * 2/3)
Thus, the total days worked to complete the work in this scenario = 18 (8 + 10)
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