Upon receipt of the application and fee the street superintendent shall apportion to each separate part of the original lot or parcel of land the proportionate part of the amount remaining unpaid on the assessment that would have been levied thereon had the lot or parcel of land been so divided at the time the original assessment was made, or shall apportion to each combined parcel the proportionate part of the amount remaining unpaid on the assessment that would have been levied thereon had the parcel been so combined at the time the original assessment was made.