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.