Equivalent weight of $Mn{O_4}^{-}$ in acidic, neutral and strong basic media are in ratio of:

$i).Mn{O_4}^{\Theta }\to M{n}^{2+}\left(acidic\right)Ew=\frac{Mw}{5}$

$ii).Mn{O_4}^{\Theta }\to Mn{O}_2\left(neutral\right)Ew=\frac{Mw}{3}$

$iii).Mn{O_4}^{\Theta }\to Mn{O_4}^{2-}\left(basic\right)Ew=\frac{Mw}{1}$

Ratio is $\frac{1}{5}:\frac{1}{3}:\frac{1}{1}=3:5:15$