ram works 8 days shyam and ghansyam his work 12 days solve this
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Ram can do a piece of work in 8 days which syam can finsih : Quant Question Archive [LOCKED]
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sravan_m444
Feb 5, 2007
Ram can do a piece of work in 8 days which syam can finsih in 12 days.If they work at it on alternate days,with Ram begining,in how many days,the work will be finished?
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devilmirror
Feb 5, 2007
sravan_m444 wrote:Ram can do a piece of work in 8 days which syam can finsih in 12 days.If they work at it on alternate days,with Ram begining,in how many days,the work will be finished?
Ram's Work Rate = R = 1/8 (work/day)
Syam's Work Rate = S = 1/12 (work/day)
Before the job is done, if Ram work n days, Syam will also works n days.
Therefore, work done by Ram = n/8 work
work done by Syam = n/12
As mentioned above that both work is not done, we can write this statement
n/8 + n/12 <= 1
n* ((3+2)/24) <= 1
n <= 24/5
n <= 4.8 days
This means that Ram and Syam will have to work at least 4 days each before the job can be done.
Work from Ram = 4 * 1/8 = 1/2
Work from Syam = 4 * 1/12 = 1/3
Total = 1/2 + 1/3 = 5/6
On 8th day, the job remain 1 - 5/6 = 1/6 work
On 9th day, Ram will work on this day and the job remain = 1/6 - 1/8 = 1/24.
On the 10th day, Syam will do the rest and the job is done.
Therefore, it will take 10 days to finish the job.
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devilmirror
Feb 5, 2007
Here is another approach for this question.
R = 1/8 (work/day)
S = 1/12 (work/day)
If they work together, their work rate = (1/8 + 1/12) = 5/24 (work/day)
They will need 24/5 (day/work) = 4.8 days to finish one work.
But since Ram and Syam will work on alternate day they will need total of 4.8 x 2 = 9.6 days = 10 days to finish the work.
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ggarr
Feb 5, 2007
Ram can do a piece of work in 8 days which syam can finsih in 12 days.If they work at it on alternate days,with Ram begining,in how many days,the work will be finished?
Ram
rt = w
r(8) = 1
r= 1/8
Syam
rt = w
r(12) = 1
r=1/2
1/8 + 1/12 = 5/24
5/24(x) = 1
****remember, 5/24 is really 1/8 + 1/12, in other words, 2 days****
x = 4.8
4.8*2 = 9.6 = 10 days
Kudos
amorpheus
Feb 5, 2007
R can do 1/8 of the job in 1 day
S can do 1/12 off the job in 1 day
If R and S both worked together for a day they can finish (1/8 + 1/12) of the job
meaning 5/24 of the job can be done in 1 day
Therefore to do 1 jobit will take 24/5 days = 4.8 days
Since both are working alternate days it will take twice as long, meaning 2(4.8) days = 9.6 = 10 days.

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Ram can do a piece of work in 8 days which syam can finsih : Quant Question Archive [LOCKED]
Topic Discussion
Page 1 of 1
sravan_m444
Feb 5, 2007
Ram can do a piece of work in 8 days which syam can finsih in 12 days.If they work at it on alternate days,with Ram begining,in how many days,the work will be finished?
--== Message from GMAT Club Team ==--
This is not a quality discussion. It has been retired.
If you would like to discuss this question please re-post it in the respective forum. Thank you!
To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
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devilmirror
Feb 5, 2007
sravan_m444 wrote:Ram can do a piece of work in 8 days which syam can finsih in 12 days.If they work at it on alternate days,with Ram begining,in how many days,the work will be finished?
Ram's Work Rate = R = 1/8 (work/day)
Syam's Work Rate = S = 1/12 (work/day)
Before the job is done, if Ram work n days, Syam will also works n days.
Therefore, work done by Ram = n/8 work
work done by Syam = n/12
As mentioned above that both work is not done, we can write this statement
n/8 + n/12 <= 1
n* ((3+2)/24) <= 1
n <= 24/5
n <= 4.8 days
This means that Ram and Syam will have to work at least 4 days each before the job can be done.
Work from Ram = 4 * 1/8 = 1/2
Work from Syam = 4 * 1/12 = 1/3
Total = 1/2 + 1/3 = 5/6
On 8th day, the job remain 1 - 5/6 = 1/6 work
On 9th day, Ram will work on this day and the job remain = 1/6 - 1/8 = 1/24.
On the 10th day, Syam will do the rest and the job is done.
Therefore, it will take 10 days to finish the job.
Kudos
devilmirror
Feb 5, 2007
Here is another approach for this question.
R = 1/8 (work/day)
S = 1/12 (work/day)
If they work together, their work rate = (1/8 + 1/12) = 5/24 (work/day)
They will need 24/5 (day/work) = 4.8 days to finish one work.
But since Ram and Syam will work on alternate day they will need total of 4.8 x 2 = 9.6 days = 10 days to finish the work.
Kudos
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ggarr
Feb 5, 2007
Ram can do a piece of work in 8 days which syam can finsih in 12 days.If they work at it on alternate days,with Ram begining,in how many days,the work will be finished?
Ram
rt = w
r(8) = 1
r= 1/8
Syam
rt = w
r(12) = 1
r=1/2
1/8 + 1/12 = 5/24
5/24(x) = 1
****remember, 5/24 is really 1/8 + 1/12, in other words, 2 days****
x = 4.8
4.8*2 = 9.6 = 10 days
Kudos
amorpheus
Feb 5, 2007
R can do 1/8 of the job in 1 day
S can do 1/12 off the job in 1 day
If R and S both worked together for a day they can finish (1/8 + 1/12) of the job
meaning 5/24 of the job can be done in 1 day
Therefore to do 1 jobit will take 24/5 days = 4.8 days
Since both are working alternate days it will take twice as long, meaning 2(4.8) days = 9.6 = 10 days.
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