Numbers of boys and girls are 'x' and 'y' respectively ; average ages of a girl and a boy are 'a' years and 'b' years respectively. The average age (in years) of all boys and girls.

A

$$\frac{x+y}{bx+ay}$$

B

$$\frac{bx+ay}{x+y}$$

C

$$\frac{ax+by}{x+y}$$

D

$$\frac{x+b}{ax+by}$$