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by gmatmachoman » Mon May 10, 2010 3:49 am
A takes twice as long as B and C together to complete a job.While B takes thrice the time taken by A & C. If all three of them worked, the work would get completed in 60 days. If all three worked together, what portion of the work was completed by C??

a . 1/2

b .3/14

c. 5/12

d. 1/4

e. 1/6
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by sanju09 » Mon May 10, 2010 4:25 am
gmatmachoman wrote:A takes twice as long as B and C together to complete a job.While B takes thrice the time taken by A & C. If all three of them worked, the work would get completed in 60 days. If all three worked together, what portion of the work was completed by C??

a . 1/2

b .3/14

c. 5/12

d. 1/4

e. 1/6
kya govind babu...

If A takes a days, B takes b days, and C takes c days, to complete the work on their lone capacities then

a = 2 b c/(b + c), b = 3 a c/(a + c), and 1/a + 1/b + 1/c = 1/60

aur bataau.n?
The mind is everything. What you think you become. -Lord Buddha



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by clock60 » Mon May 10, 2010 5:45 am
gmatmachoman wrote:A takes twice as long as B and C together to complete a job.While B takes thrice the time taken by A & C. If all three of them worked, the work would get completed in 60 days. If all three worked together, what portion of the work was completed by C??

a . 1/2

b .3/14

c. 5/12

d. 1/4

e. 1/6
hard work, not sure that it is gmat problem, as it is impossible to solve in decent time period

a=2*(bc/(b+c))
b=3*(ac/(a+c))
(1/a+1/b+1/c)*60=1

1/a+1/b+1/c=1/60
1/a+(b+c)/bc=1/60
a/2=bc/(b+c).
2/a=(b+c)/bc
1/a+2/a=1/60
a=180

1/a+1/c+1/b=1/60
(a+c)/ac+1/b=1/60.
b/3=ac/(a+c)
3/b=(a+c)/ac
3/b+1/b=1/60
b=240

1/180+1/240+1/c=1/60
1/c=5/720

1/a+1/b+1/c=12/720
(5/720)/(12/720)=5/12
so C
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by harshavardhanc » Mon May 10, 2010 6:02 am
clock60 wrote:
gmatmachoman wrote:A takes twice as long as B and C together to complete a job.While B takes thrice the time taken by A & C. If all three of them worked, the work would get completed in 60 days. If all three worked together, what portion of the work was completed by C??

a . 1/2

b .3/14

c. 5/12

d. 1/4

e. 1/6
hard work, not sure that it is gmat problem, as it is impossible to solve in decent time period

a=2*(bc/(b+c))
b=3*(ac/(a+c))
(1/a+1/b+1/c)*60=1

1/a+1/b+1/c=1/60
1/a+(b+c)/bc=1/60
a/2=bc/(b+c).
2/a=(b+c)/bc
1/a+2/a=1/60
a=180

1/a+1/c+1/b=1/60
(a+c)/ac+1/b=1/60.
b/3=ac/(a+c)
3/b=(a+c)/ac
3/b+1/b=1/60
b=240

1/180+1/240+1/c=1/60
1/c=5/720

1/a+1/b+1/c=12/720
(5/720)/(12/720)=5/12
so C
a short-cut, hope you like it.

think in terms of rate.

First condition :

A takes twice the time as B& C together, means that if A's rate is x , B+C's is 2x

hence, 3x=1/60 or x=1/180 or A takes 180 days to complete.

Second condition :

B takes twice the time as A& C together, means that if B's rate is y , A+C is 3y

or 4y= 1/60 or y = 1/240 or B takes 240 days to complete.

therefore, C's rate or the per day work of C = 1/60 (1-1/3-1/4) = 5/720

or in 60 days, C will complete 60 * 5/720 = 5/12th of the total work . Option C ;)
Regards,
Harsha
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by sanju09 » Mon May 10, 2010 6:05 am
harshavardhanc wrote:
clock60 wrote:
gmatmachoman wrote:A takes twice as long as B and C together to complete a job.While B takes thrice the time taken by A & C. If all three of them worked, the work would get completed in 60 days. If all three worked together, what portion of the work was completed by C??

a . 1/2

b .3/14

c. 5/12

d. 1/4

e. 1/6
hard work, not sure that it is gmat problem, as it is impossible to solve in decent time period

a=2*(bc/(b+c))
b=3*(ac/(a+c))
(1/a+1/b+1/c)*60=1

1/a+1/b+1/c=1/60
1/a+(b+c)/bc=1/60
a/2=bc/(b+c).
2/a=(b+c)/bc
1/a+2/a=1/60
a=180

1/a+1/c+1/b=1/60
(a+c)/ac+1/b=1/60.
b/3=ac/(a+c)
3/b=(a+c)/ac
3/b+1/b=1/60
b=240

1/180+1/240+1/c=1/60
1/c=5/720

1/a+1/b+1/c=12/720
(5/720)/(12/720)=5/12
so C
a short-cut, hope you like it.

think in terms of rate.

First condition :

A takes twice the time as B& C together, means that if A's rate is x , B+C's is 2x

hence, 3x=1/60 or x=1/180 or A takes 180 days to complete.

Second condition :

B takes twice the time as A& C together, means that if B's rate is y , A+C is 3y

or 4y= 1/60 or y = 1/240 or B takes 240 days to complete.

therefore, C's rate or the per day work of C = 1/60 (1-1/3-1/4) = 5/720

or in 60 days, C will complete 60 * 5/720 = 5/12th of the total work . Option C ;)
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www.manyagroup.com
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by clock60 » Mon May 10, 2010 6:48 am
great work Harsha
thank you for sharing this!
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by kstv » Mon May 10, 2010 7:17 am
2/a = 1/b+1/c ...1
3/b = 1/a+1/c ...2
1/a+1/b+1/c = 1/60
2/a= 1/60-1/a 2 + 1 =a/60
a = 180
3/b = 1/60- 1/b 3+1 = b/60
b = 240
just saw Harsh's method , much better
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by gmatmachoman » Mon May 10, 2010 7:22 am
Harsha Bhai !!

wow wow wow !!! U need a standing ovation man!! yeah its CAT wala....I was expecting U /Liferock/kstv/pheonix/sanju to solve...

But ur was just too good ..well done bro..

I dont think this much wil come for GMAT......Anyways..Thx guys for pitching in!!
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by liferocks » Mon May 10, 2010 7:40 am
A takes twice as long as B and C together to complete a job..so in same time A does 1/3 of job and b n c 2/3rd
B takes thrice the time taken by A & C so in same time B does 1/4 the of the job done and A n C does 3/4

so when they work together A and B does 1/3+1/4=7/12

C does 1-7/12=5/12..that 60 days is irrelevant

Ans option C
"If you don't know where you are going, any road will get you there."
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by govind_raj_76 » Tue May 11, 2010 9:46 pm
harshavardhanc wrote:
clock60 wrote:
gmatmachoman wrote:A takes twice as long as B and C together to complete a job.While B takes thrice the time taken by A & C. If all three of them worked, the work would get completed in 60 days. If all three worked together, what portion of the work was completed by C??

a . 1/2

b .3/14

c. 5/12

d. 1/4

e. 1/6
hard work, not sure that it is gmat problem, as it is impossible to solve in decent time period

a=2*(bc/(b+c))
b=3*(ac/(a+c))
(1/a+1/b+1/c)*60=1

1/a+1/b+1/c=1/60
1/a+(b+c)/bc=1/60
a/2=bc/(b+c).
2/a=(b+c)/bc
1/a+2/a=1/60
a=180

1/a+1/c+1/b=1/60
(a+c)/ac+1/b=1/60.
b/3=ac/(a+c)
3/b=(a+c)/ac
3/b+1/b=1/60
b=240

1/180+1/240+1/c=1/60
1/c=5/720

1/a+1/b+1/c=12/720
(5/720)/(12/720)=5/12
so C
a short-cut, hope you like it.

think in terms of rate.

First condition :

A takes twice the time as B& C together, means that if A's rate is x , B+C's is 2x

hence, 3x=1/60 or x=1/180 or A takes 180 days to complete.

Second condition :

B takes twice the time as A& C together, means that if B's rate is y , A+C is 3y

or 4y= 1/60 or y = 1/240 or B takes 240 days to complete.

therefore, C's rate or the per day work of C = 1/60 (1-1/3-1/4) = 5/720

or in 60 days, C will complete 60 * 5/720 = 5/12th of the total work . Option C ;)
How did u get this equation below ??

C's rate or the per day work of C = 1/60 (1-1/3-1/4) = 5/720 (Could u please explain ?? ). Thanks
Govind
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by mj78ind » Wed May 12, 2010 1:30 am
Hi Raj,

I have a slightly different approach. Let's assume the work is 120 units, the rate of work is a = a units/day, b = b units/day and c.

Now,
120/a = 2{120/(b+c)} ------- 1

120/b = 3{120/(a+c)} ------- 2

120/(a+b+c) = 60 ------------- 3

If we solve eqtns 1 and 2 only, to get 'c' and 'a' in terms of 'b', we get:

a = (4/3)b, c = (5/3)b.

Now we can solve, c/(a+b+c) = {(5/3)b}/[{(5/3)b} + b + {(4/3)b}] = 5/12

Hence choice C
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