In the redox reaction: xKMnO₄ + yNH₃ → KNO₃ + MnO₂ + KOH + H₂O

aKMnO₄ + bNH₃ $\to$ KNO₃ + MnO₂ + KOH + H₂O

$\stackrel{+7}{\mathrm{Mn}}{\mathrm{O}}_4^{-}\to \stackrel{+4}{\mathrm{Mn}}{\mathrm{O}}_2$

Decrease in Ox.no = 3
$\stackrel{-3}{\mathrm{N}}{\mathrm{H}}_3\to \stackrel{+5}{{\mathrm{NO}}_3^{-}}$

decrease in ox.no=8
Criss cross method
8 MnO₄^- + 3NH₃
x = 8 and y = 3