Compound $A$ was prepared by oxidation of compound $B$ with alkaline $KMnO_4$. Compound $A$ on reduction with lithium aluminium hydride $(LiAlH_4)$ gets converted back to compound $B$. When compound $A$ is heated with compound $B$ in the presence of $H_2SO_4$,it produces a fruity smell of compound $C$. To which family do the compounds $A$,$B$,and $C$ belong?

• A
  $A$: Carboxylic acid,$B$: Alcohol,$C$: Ester
• B
  $A$: Alcohol,$B$: Carboxylic acid,$C$: Ester
• C
  $A$: Aldehyde,$B$: Alcohol,$C$: Ester
• D
  $A$: Carboxylic acid,$B$: Aldehyde,$C$: Ester