The correct option is A (III) > (I) > (II) > (IV)
In presence of aprotic polar solvent, the reaction will go by SN2 mechanism. In this, the nucleophile will attack the substrate from the back to form a transition state and then the bond between C and leaving group breaks to form the product.
Good leaving group favours the rate of SN2 reaction. A good leaving group must have a weak C-X bond.
The bond between C and I is so weak due to the larger size of I and it is highly reactive for SN2 reaction.
The C−F bond is too strong to break during SN2 reaction.
Therefore, based on the bond strength between C−X, the increasing order of preference of alkyl halides for SN2 reaction is
R−F<R−Cl<R−Br<RI
Hence, the decreasing order of rate of reaction is
(III) > (I) > (II) > (IV)