Any person owning an undivided share or other part of any parcel of real property, assessed in one description, may pay on the share or part thus owned by paying an amount having the same relation to the whole tax as the value of the part on which payments is made has to the value of the whole parcel. The person making such payment shall accurately describe the part or share on which he makes payment and the receipt given and the record of the receiving officers shall show such description and by whom paid; and in cases of the sale of the remaining part or share, for nonpayment of taxes, he may purchase the same in like manner as any disinterested person could. The values above referred to shall be determined by the Assessor who before making such determination shall set a time for hearing and shall notify the interested parties by registered mail at their last known addresses, such notice to be mailed at least ten (10) days before the hearing. Any person aggrieved by such determination may appeal therefrom to the Board of Review by filing notice thereof with the Clerk within ten (10) days after receiving notice of such decision. The Board of Review shall then without delay meet and review such decision and either affirm or modify it.