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Work and rate

by GMATMadeEasy » Fri Oct 08, 2010 2:38 pm
A and B can do a work together in 18 days, B and C in 24, and A and C in 36. They all work together for 4 days and then A left. In how many more days can B and C finish the remaining work?
(A) 6
(B) 8
(C) 12
(D)16
(E) 18


What is the fastest way to solve this problem ?
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by sanabk » Fri Oct 08, 2010 3:55 pm
E

A, B work together in 18 days => A+B=18 days => A+B = (1/18)th work in 1 day
B, C work together in 24 days => B+C=24 days => B+C = (1/24)th work in 1 day
C, A work together in 36 days => C+A=36 days => C+A = (1/36)th work in 1 day
--------------------
2(A+B+C) = (9/72)th work in 1 day
(A+B+C) = (9/144)th work in 1 day
(A+B+C) = 4*(9/144)th work in 4 days = (1/4)th work in 4 days

After A+B+C working for 4 days the part of work remaining is 1-(1/4)=(3/4)th work

B+C = (1/24)th work in 1 day
(3/4)th work will take = (3/4)/(1/24)=18 days
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by diebeatsthegmat » Fri Oct 08, 2010 6:54 pm
sanabk wrote:E

A, B work together in 18 days => A+B=18 days => A+B = (1/18)th work in 1 day
B, C work together in 24 days => B+C=24 days => B+C = (1/24)th work in 1 day
C, A work together in 36 days => C+A=36 days => C+A = (1/36)th work in 1 day
--------------------
2(A+B+C) = (9/72)th work in 1 day
(A+B+C) = (9/144)th work in 1 day
(A+B+C) = 4*(9/144)th work in 4 days = (1/4)th work in 4 days

After A+B+C working for 4 days the part of work remaining is 1-(1/4)=(3/4)th work

B+C = (1/24)th work in 1 day
(3/4)th work will take = (3/4)/(1/24)=18 days
wow.... this is so complicating....
1/a+1/b=1/18
1/b+1/c=1/24
1/c+1/a=1/36
add them above all together <=> 2(1/a+1/b+1/c)=9/72 thus together they finish the work in 16 days
so in h4 days they only finish 1/4 job and 3/4 job leff is for B+C
b+c finish 1 work in 24 days thus they will do 24*3/4=18 days to finish the left job.
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by neerajkumar1_1 » Fri Oct 08, 2010 7:05 pm
diebeatsthegmat wrote:
sanabk wrote:E

A, B work together in 18 days => A+B=18 days => A+B = (1/18)th work in 1 day
B, C work together in 24 days => B+C=24 days => B+C = (1/24)th work in 1 day
C, A work together in 36 days => C+A=36 days => C+A = (1/36)th work in 1 day
--------------------
2(A+B+C) = (9/72)th work in 1 day
(A+B+C) = (9/144)th work in 1 day
(A+B+C) = 4*(9/144)th work in 4 days = (1/4)th work in 4 days

After A+B+C working for 4 days the part of work remaining is 1-(1/4)=(3/4)th work

B+C = (1/24)th work in 1 day
(3/4)th work will take = (3/4)/(1/24)=18 days
wow.... this is so complicating....
1/a+1/b=1/18
1/b+1/c=1/24
1/c+1/a=1/36
add them above all together <=> 2(1/a+1/b+1/c)=9/72 thus together they finish the work in 16 days
so in h4 days they only finish 1/4 job and 3/4 job leff is for B+C
b+c finish 1 work in 24 days thus they will do 24*3/4=18 days to finish the left job.
its not complicated as such...
ofcourse when u attack such a question for the first time, it seems complicated.. ..

but remember the way this problem is solved and the logic been used behind it..

the question could also ask you that how much time would each of them take individually to complete the work... in which case after u get the combined rate... all u need to do is:
say work time for A = total - (time of B and C)

total u already found out..
time of B and C is given to you...

u can follow the same method for the rest of them..

Hope this further Helps! .. :)
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by Yanat » Fri Oct 08, 2010 9:56 pm
A and B can do a work together in 18 days, B and C in 24, and A and C in 36. They all work together for 4 days and then A left. In how many more days can B and C finish the remaining work?
(A) 6
(B) 8
(C) 12
(D)16
(E) 18

A+B in one day = 1/18 of work
B+C in one day = 1/24 of work
A+C in one day = 1/36 of work

So In 4 days A+B+C = 1/4 of work. Now A leaves. So we have B+C left. Now pending work is 1-1/4= 3/4

If B+C in one day = 1/24 of work, so B+C can complete 3/4 of the work in 18 days.

IMO it is E.

Can someone post the correct answer
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by GMATGuruNY » Sat Oct 09, 2010 4:16 am
GMATMadeEasy wrote:A and B can do a work together in 18 days, B and C in 24, and A and C in 36. They all work together for 4 days and then A left. In how many more days can B and C finish the remaining work?
(A) 6
(B) 8
(C) 12
(D)16
(E) 18


What is the fastest way to solve this problem ?
When the job is undefined, plug in!

Plug in job = 72.
Rate for A+B = w/t = 72/18 = 4.
Rate for B+C = w/t = 72/24 = 3.
Rate for A+C = w/t = 72/36 = 2.
Combining the rates, we get:
(A+B) + (B+C) + (A+C) = 4+3+2
2A + 2B + 2C = 9
A+B+C = 9/2
Work completed in 4 days = r*t = 9/2 * 4 = 18.
Remaining work = 72-18 = 54.
Time for B+C to finish = w/r = 54/3 = 18.

The correct answer is E.
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