Compound A should be
\(CH_3 - \underset{(A)}{\overset{O}{\overset{||}C}}- O + C_2H_5\)
A undergoes acid hydrolysis to form acetic acid and ethanol as follows
\(CH_3 - \overset{O} {\overset{||}C} - O \ C_2 H_5 \xrightarrow{H_3O^+} \underset{(B)}{CH_3COOH}+\underset{(C)}{ C_2H_5OH}\)
Ethanol on oxidation with acidified potassium permanganate gives acetic acid
\(C_2H_5OH \xrightarrow{KMnO_4/H^+} CH_3COOH\)
Sodium salt of B i.e. CH3COONa gives methane on heating with soda lime as follows
\(CH_3COONa \underset{\Delta} {\xrightarrow {Soda lime}}CH_4\)
Boiling point of acetic acid (B) is \(118^\circ C\) whereas that of ethanol (C) is \(78^\circ C\). This is because acetic acid has intermolecular hydrogen bonding.