If the average of $p$ numbers is $q^2$ and that of $q$ numbers is $p^2$, then the average of $(p+q)$ numbers is:

$pq$

average of p numbers = q²

Sum of p numbers = pq²

average of q numbers = p²

Sum of q numbers = qp²

average of p+q numbers = (Sum of p+q numbers)/(p+q) = (pq²+qp²)/(p+q) = pq(p+q)/(p+q) = pq

The correct answer is Option (3) → $pq$