'A' takes twice as much time as 'B' to complete a work and 'C' does it in the…

Let the time taken by B alone be x days. Since A takes twice as much time, A requires 2x days. The work rate of B is 1/x per day, and the work rate of A is 1/(2x) per day. C completes the work in the same time as A and B together, meaning C's rate is the sum of their individual rates: 1/(2x) + 1/x = 3/(2x). Therefore, C alone would take (2x/3) days. When all three work together, their combined rate is the sum of individual rates: 1/(2x) + 1/x + 3/(2x). Simplifying this expression gives (1+2+3)/(2x) = 6/(2x) = 3/x. We are told they complete the work in 5 days, so their combined rate is also 1/5. Equating these rates: 3/x = 1/5, which leads to x = 15. Thus, B takes 15 days alone. Option A (12 days) and Option D (18 days) are incorrect because they do not satisfy the combined rate equation derived from the problem statement.