$\frac{ H _{2} O _{2}+2 e ^{-} \rightarrow 2 HO ^{\ominus}}{2 Fe ^{2+}+ H _{2} O _{2} \rightarrow 2 Fe ^{3+}+2 HO _{(q\omega)}^{\ominus}}$

$x =2 \quad y =2$

$\left[8 H ^{+}+ MnO _{4}^{-}+5 e ^{-} \rightarrow Mn ^{2+}+4 H _{2} O \right] \times 2$

$\left[ H _{2} O _{2} \rightarrow O _{2( g )}+2 H ^{+}+2 e ^{-}\right] \times 5$

$\Rightarrow 16 H ^{+}+2 MnO _{4}^{-}+5 H _{2} O _{2}$

$\rightarrow 2 Mn ^{2+}+8 H _{2} O +5 O _{2(g)}+10 H ^{+}$

$\Rightarrow 6 H ^{+}+2 MnO _{4}^{-}+5 H _{2} O _{2}$

$\rightarrow 2 Mn ^{2+}+8 H _{2} O +5 O _{2( g )}$

So $\quad x^{\prime}=2 \quad y^{\prime}=8 \quad z^{\prime}=5$

so $\quad x+y+x^{\prime}+y^{\prime}+z^{\prime}$

$\Rightarrow 2+2+2+8+5$

$\Rightarrow 19$