Mathematics Question from JEE Main 2023 · 12 April, Shift 1

Let the positive numbers $a_1, a_2, a_3, a_4$, and $a_5$ be in a G.P. Let their mean and variance be $\frac{31}{10}$ and $\frac{m}{n}$, respectively, where $m$ and $n$ are co-prime. If the mean of their reciprocals is $\frac{31}{40}$ and $a_3 + a_4 + a_5 = 14$, then $m + n$ is equal to: