If A and B can do a piece of work in 20 days,and A alone can do the same work in 30 days, then in how many days can B alone complete the same work?

Given, 

A and B together can do the work in 20 days.

A alone can do the work in 30 days 

Let the total work be 60 ( LCM of 20 & 30)

Efficiency = $$\frac{\ Total\ work}{time\ taken}\ $$

Efficiency of (A + B) = $$\frac{60}{20}=\ 3$$

Efficiency of A alone = $$\frac{60}{30}=2$$

so, Efficiency of B = Efficiency of (A+B) - Efficiency of A

i.e; 3 - 2 = 1

Time in which B alone can complete the work = $$\frac{60}{1}=60\ days$$

Hence, option A is correct.