# Aptitude Question ID : 94170

The average of x numbers is $y^{2}$ and the average of y numbers is $x^{2}$. So the average of all the numbers taken together is:
[A]$xy$
[B]$xy^{2}+yx^{2}$
[C]$\frac{x^{2}+y^{2}}{x+y}$
[D]$\frac{x^{3}+y^{3}}{x+y}$

$\mathbf{xy}$
Total sum of x numbers $= xy^{2}$
Total sum of y numbers $= yx^{2}$
∴ Required Average =
$= \frac{xy^{2}+yx^{2}}{x+y}$
$= \frac{xy(y+x)}{x+y} = xy$
Hence option [A] is the right answer.