Which of the following samples of reducing agents is/are chemically equivalent to $25 \mathrm{ml}$ of $0.2 \mathrm{N} {\mathrm{KMnO}}_4$ to be reduced to ${\mathrm{Mn}}^{+2}$and water? 

Hydrogen peroxide in aqueous solution decomposes on warming to give oxygen according to the equation: $2{\mathrm{H}}_2{\mathrm{O}}_2\left(\mathrm{aq}\right)⟶2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)+{\mathrm{O}}_2 \left(\mathrm{g}\right)$ under conditions where $1$ mole of gas occupies $24{\mathrm{dm}}^3$. $100 {\mathrm{cm}}^3$ of $\mathrm{XM}$ solution of ${\mathrm{H}}_2{\mathrm{O}}_2$ produces $3{\mathrm{dm}}^3$ of ${\mathrm{O}}_2$. Thus, $\mathrm{X}$ is:

${\mathrm{H}}_2{\mathrm{O}}_2$ acts as both oxidising as well as reducing agent. As oxidising agent, its product is ${\mathrm{H}}_2\mathrm{O},$ but as reducing agent, its product is ${\mathrm{O}}_2.$ Volume strength has great significance for chemical reactions.

The strength of  $\text{'}10\mathrm{V}\text{'}$ means $1$ volume (or litre) of ${\mathrm{H}}_2{\mathrm{O}}_2$ on decomposition $\left({\mathrm{H}}_2{\mathrm{O}}_2\to {\mathrm{H}}_2\mathrm{O}+\frac{1}{2}{\mathrm{O}}_2\right)$ gives $10$ volume (or litre) of oxygen at $\mathrm{NTP}.$

$15\mathrm{gmBa}{\left({\mathrm{MnO}}_4\right)}_2$ sample containing inert impurity is completely reacting with $100 \mathrm{ml}$ of $\text{'}11.2 \mathrm{V}\text{'}{\mathrm{H}}_2{\mathrm{O}}_2,$ in acidic medium then what will be the $\%$ purity of $\mathrm{Ba}{\left({\mathrm{MnO}}_4\right)}_2$ in the sample?

(Atomic mas $\mathrm{Ba}=137, \mathrm{Mn}=55$)