SMO 2015 Senior Round 1 Question 3

Suppose $m$ and $n$ are real numbers such that the roots of the equation $2x^2-mx+8=0$ are $\alpha$ and $\beta$ while the roots of the equation $5x^2-10x+5n=0$ are $\dfrac1\alpha$ and $\dfrac1\beta$. Find the value of $mn$.