When any tract less than the whole parcel designated for taxation and bid in for the state shall be taken or encumbered by such eminent domain proceedings, the tract so taken or encumbered may be redeemed and the delinquent taxes and assessments thereon discharged, as provided in sections 281.39 and 281.40, without redeeming or discharging the delinquent taxes and assessments on the entire parcel so bid in for the state. When only such portion or fraction of the parcel bid in for the state shall be redeemed and discharged from taxes and assessments, the amount to be paid for such redemption and discharge from delinquent taxes and assessments shall be computed by the auditor of the county wherein such lands are situated, and shall be such a part or proportion of the amount designated by any such law permitting redemption and discharge on payment of a fraction or percentage of the total amount due, as provided in sections 281.39 and 281.40, as the tract taken or encumbered by the proceedings and so redeemed bears to the value of the entire parcel bid in for the state, and of which it forms a part. Any party interested in such computation and determination of value, and aggrieved thereby, may, within ten days following the filing thereof, appeal to the district court of the county wherein such land is situated, by filing written notice of such appeal and proof of service thereof, with the court administrator of such court.