Ram can do a piece of work in 8 days which syam can finsih

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Ram can do a piece of work in 8 days which syam can finsih [#permalink]

05 Feb 2007, 11:34

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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Re: Ram and Shyam [#permalink]

05 Feb 2007, 13:59

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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[#permalink]

05 Feb 2007, 14:04

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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[#permalink]

05 Feb 2007, 14:11

Quote:

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

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[#permalink]

05 Feb 2007, 14:40

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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[#permalink]

05 Feb 2007, 21:52

We know that it will take more than 8 days because that is how long R alone can do the job. So R 5d ays and S 4 days = 5/8 + 1/3 = 23/24.

Therefore we need one more day or 10.

This isn't has fast as the other guys, but if you are math moron like me it gets the job done.

[#permalink] 05 Feb 2007, 21:52

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Ram can do a piece of work in 8 days which syam can finsih

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Ram can do a piece of work in 8 days which syam can finsih

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