A, B and C have 40, x and y balls, respectively. If B gives 20 balls to A, he is left with half as many balls as C. If together they had 60 more balls, each of them would have had 100 balls on an average. What is the ratio of x to y?

If together they had 60 more balls, each of them would have had 100 balls on an average,

$$\frac{40 + X + Y + 60}{3} = 100$$

$$X + Y + 100 = 300 \Rightarrow X + Y = 200$$.........(1)

If B gives 20 balls to A, he is left with half as many balls as C,

$$X - 20 = \frac{1}{2}Y$$

$$2X - 40 = Y$$ (or) $$2X - Y = 40$$..................(2)

Add equations (1) and (2) 

$$3X = 240$$ (or) $$X = 80$$

Substitute $$X$$ value in equation (1)

$$80 + Y = 200$$ (or) $$Y = 120$$

$$X : Y = 80 : 120$$ (or) $$2:3$$

Hence, option B is the correct answer.