The average of x numbers is y² and the average of y numbers is x². So, the average of all the numbers taken together is :

Solution (By Examveda Team)

According to the question,
Average of x number is y²
∴ Sum of x number is = xy²
Average of y number is = x²
∴ Sum of y number is = yx²
Average of all number is
= $$\frac{{{xy^2} + {yx^2}}}{{x + y}}$$
= $$\frac{{xy\left( {x + y} \right)}}{{x + y}}$$
= xy