In case a mortgage, lien, or sheriff’s certificate, or any other instrument conveying an interest in property, affects only a part of the real estate taxed as a unit, any person interested therein may petition the county auditor that the person be permitted to pay taxes and satisfy any outstanding tax lien as to that part only of the real estate in which the party is interested. Such petition must set forth the petitioner’s interest in the property. It must be verified and may be in the form of an affidavit. Immediately upon the receipt of such petition, the county auditor shall consider the same and shall make a fair and equitable valuation of the whole tract. The county auditor shall apportion to the petitioner a part of the taxes, interest, and penalty to be paid by the petitioner in order to effect satisfaction, which must bear to the taxes, special assessments, interest, penalty, and costs accrued on the whole tract the ratio which the value of the part or parcel of land in which the petitioner claims an interest bears to the value of the entire assessed tract of land. Thereupon the county auditor, by certified mail, shall notify all persons interested in such real property according to the record, either as owner or as the holder of a mortgage or other lien or sheriff’s certificate, of the filing of such petition and of the auditor’s assessment of such tract or parcel of land and of the auditor’s apportionment of the taxes thereon, and the date when the same will be considered and heard by the auditor. Such hearing may not be less than ten days after the mailing of such notice. Upon the date set, the county auditor shall hear the parties interested and shall assess such tract and apportion the taxes thereon as the auditor deems fair and equitable.