The thing about this type of question is the fact that a piece of work takes less time the more people are involved. It's a case of inverse proportionality. To make the problem one of direct proportionality, consider inverting the problem. How much of the work can be done in a day? If it takes n days to do a job, then in 1 day an nth of the job can be done, 1/n. Two people doing the same job contribute a proportion of the job each.
Let's say A takes a days to do a job, B takes b days, and C takes c days. Then A does 1/a of the job in a day, B 1/b and C 1/c. A and B together do 1/a+1/b of the job in a day. If the job takes 3 days then in one day 1/3 job has to be done, so 1/a+1/b=1/3; similarly 1/b+1/c=1/4 and 1/c+1/a=1/4. If we add these equations together we get 2/a+2/b+2/c=1/3+1/4+1/4=5/6, so 1/a+1/b+1/c=5/12. But we know 1/b+1/c=1/4, so 1/a+1/4=5/12, making 1/a=5/12-1/4=2/12=1/6, and a=6. 1/a+1/b=1/3 so 1/c=5/12-1/3=1/12, and c=12 days.