I have positive real random numbers $u_1,\ldots,u_n$ and $v_1,\ldots,v_n$ and $x_1,\ldots,x_n$ and $y_1,\ldots,y_n$.
I know that the arithmetic mean of $u_i$'s is greater than the arithmetic mean of $x_i$'s, i.e., $$\sum_{i=1}^nu_i\geq\sum_{i=1}^nx_i,$$ and the arithmetic mean of $v_i$'s is less than the arithmetic mean of $y_i$'s, i.e., $$\sum_{i=1}^nv_i\leq\sum_{i=1}^ny_i.$$
When we can say that $$\sum_{i=1}^n\dfrac{u_i}{v_i}\leq\sum_{i=1}^n\dfrac{x_i}{y_i}?$$ because intuitively it seems that the opposite inequality should hold but that is not true (I cannot find a counterexample though). Can we say something for large $n$?