Answer :
[tex]NH^+_4+MnO^-_4\rightarrow NO^-_3+Mn^{2+}[/tex]
Now we have to balance the given redox reaction in acidic medium by half reaction method.
1st half reaction : [tex]8H^++MnO^-_4+5e^-\rightarrow Mn^{2+}+4H_2O[/tex]
2nd half reaction : [tex]3H_2O+NH^+_4\rightarrow NO^-_3+10H^++8e^-[/tex]
For net balanced reaction, 1st half reaction is multiplying by 8 and 2nd half reaction is multiplying by 5
The net balanced redox reaction is,
[tex]8MnO^-_4+14H^++5NH^+_4\rightarrow 8Mn^{2+}+17H_2O+5NO^-_3[/tex]
[tex]Cr(OH)_3+ClO^-_3\rightarrow CrO^{2-}_4+Cl^-[/tex]
Now we have to balance the given redox reaction in basic medium by half reaction method.
1st half reaction : [tex]Cr(OH)_3+H_2O+5OH^-\rightarrow CrO^{2-}_4+5H_2O+3e^-[/tex]
2nd half reaction : [tex]ClO^-_3+6H_2O+6e^-\rightarrow Cl^-+3H_2O+6OH^-[/tex]
For net balanced reaction, 1st half reaction is multiplying by 2.
The net balanced redox reaction is,
[tex]2Cr(OH)_3+ClO^-_3+4OH^-\rightarrow 2CrO^{2-}_4+Cl^-+5H_2O[/tex]