IN-TST 2010 Problem 9

Let $A=(a_{jk})$ be a $10\times 10$ array of positive real numbers such that the sum of numbers in row as well as in each column is $1$ . Show that there exists $j<k$ and $l<m$ such that $$a_{jl}a_{km}+a_{jm}a_{kl}\ge \frac{1}{50}$$