Answer is: 10
\(\underset{\text { (O.A) }}{\mathrm{KMnO}_{4}} \xrightarrow{\text { Acidic medium }} \mathrm{Mn}^{2+}\)
X is difference in oxidation state.
\( 7-2=5\)
So \(\mathrm{X}=5\)
\(6 \mathrm{CH}_{3} \mathrm{COO}^{\ominus}+\mathrm{Fe}^{3+}+\mathrm{H}_{2} \mathrm{O} \rightarrow\left[\mathrm{Fe}_{3}\left(\mathrm{OH}_{2}\right)\left(\mathrm{CH}_{3} \mathrm{COO}\right)_{6}\right]^{\oplus}+2 \mathrm{H}^{\oplus}\)
\( \left[\mathrm{Fe}_{3}(\mathrm{OH})_{2}\left(\mathrm{CH}_{3} \mathrm{COO}\right)_{6}\right]^{\oplus}+4 \mathrm{H}_{2} \mathrm{O} \rightarrow \underset{\text { Brown red ppt }}{\left[\mathrm{Fe}(\mathrm{OH})_{2}\left(\mathrm{CH}_{3} \mathrm{COO}\right]\right.}+\mathrm{CH}_{3} \mathrm{COOH}+\mathrm{H}^{\oplus}\)
\( \mathrm{Fe}^{3+} \Rightarrow 3 \mathrm{~d}^{5} 4 \mathrm{~s}^{0} \ \text{contains 5 d electrons}\)
\( So \ \mathrm{Y}=5\)
\( X+Y=5+5=10\)