The result is $\frac{41+1}{2010+49}=\frac{42}{2059}$. In general, the fraction $\frac{x}{y}$ with the smallest denominator with $\frac{a}{b}<\frac{x}{y}<\frac{c}{d}$ is $\frac{a+c}{b+d}$ whenever $bc-ad=1$. This is a familiar result from the Theory of Farey Fractions but completely straightforward to prove. Just expanding the inequalities, we get $ay<bx$ and $dx<cy$. Hence $ay \le bx-1$ and $dx \le cy-1$. Hence $ady \le bdx-d$ an $bdx \le bcy-b$. Hence $ady \le bcy-b-d$. Hence $y \ge b+d$ as desired. (Of course we also need to check that $\frac{a+c}{b+d}$ indeed satisfies the inequality chain but this is just a direct computation, in particular this part is true even without the condition $bc-ad=1$.)

It is curious that exactly the same problem was used in the 49th German Olympiad 2010. I wonder whether Mexico also had its 49th (or maybe 41st?) olympiad that year?