If A and B can do a piece of work in 20 days, and A alone can do the same work in 60 days, then in how many days can B alone complete the same work'?

Given, 

A and B together can complete the work in 20 days

B alone can finish the work in 60 days.

Let the Total work be 60 units (LCM of 20 and 60)

As we know, 

$$efficiency\ =\ \frac{total\ work}{time\ taken}$$ 

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

Efficiency of A alone = $$\frac{60}{60}=1$$

Now, Efficiency of B = 3 - 1 = 2

Time required to finish the work by alone B = $$\frac{60}{2}=30$$

Hence, Option C is correct.