Question

Ram can do a work in 18 days how did he work in a day

Answer 1

Ram's Work Rate = R = 1/8 (work/day) 


B=
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.