# The average of x numbers is y and average of y numbers is x. Then the average of all the numbers taken together is:

The average of x numbers is y and average of y numbers is x. Then the average of all the numbers taken together is:
[A]$\frac{xy}{x+y}$
[B]$\frac{x+y}{2xy}$
[C]$\frac{x^{2}+y^{2}}{x+y}$
[D]$\frac{2xy}{x+y}$

$\mathbf{\frac{2xy}{x+y}}$
Sum of x numbers = xy
Sum of y numbers = xy
∴ Required Average $= \frac{xy+xy}{x+y} = \frac{2xy}{x+y}$
Hence option [D] is the right answer.