A can complete a piece of work in 14 days, while A and B together can complete it in days. How long will B alone take to complete it?

Given: ​

Time taken by A to finish the work = 14 days 

Time taken by A and B together to finish the work = $$3\frac{1}{2}days$$​​

​$$\text{Total Work } = \text{ Efficiency } \times \text{ Total time taken}$$ 

LCM of 14 and 7 is 14 .

Total work is 14 unit 

Efficiency of B = Efficiency of {A+B} - Efficiency of A 

                         =  4 - 1 

                         = 3 units
 time taken to complete the work alone by B  = $$\frac{14}{3}$$​ days ​