The number of days to finish a work by A is double the number of days to finish the work by B. The number of days to finish the work by C is half the number of days to finish the work by B. A can finish the work in 12 days. If B works on the 1st day, A works on the 2nd day and C works on the 3rd day, again B works on the 4th day and so on, then the work is finished in _____ days.

Correct option is A

Given:
A can finish the work in 12 days.
The number of days to finish the work by A is double the number of days to finish the work by B.
The number of days to finish the work by C is half the number of days to finish the work by B.
B works on the 1st day, A works on the 2nd day, and C works on the 3rd day, and this cycle repeats.
Concept Used:
We use the LCM method to find the total number of days required to finish the work when three people work alternately.
We find the work done per person per day and then calculate the total work done in one cycle (3 days)
Solution:
Since, A can finish the work in 12 days.
B finishes the work in $$\frac{12}{2}=$$​ 6 days.

C finishes the work in $$\frac 62 =3$$ days.
Total Work = LCM of 12, 6 and 3 = 12 unit
Efficiency of A, B and C = $$\frac{12}{12} = 1\, \text{unit per day}, \frac{12}{6} = 2 \, \text{unit per day}, \frac{12}{3} = 4 \, \text{unit per day}$$ respectively. 
As B works on first day = 2 unit of work completed
Then A works on second day = 1 unit of work completed
Then, C works on third day = 4 unit of work completed 
In 3 days, 7 unit of work completed
Remaining Work = 12-7= 5 unit  
Now, the 4th day will be completed by B = 2 unit of work
5th day work will be done by A = 1 unit of work 
Remaining 2 unit of work will be completed by C in = $$\frac{2}{4} = 0.5$$ days
Total Time Taken to complete the whole work  = 5+ 0.5 = 5.5 days

​