Section 112. If before five o’clock in the afternoon of the second day next succeeding the day of a caucus, ten or more voters of any town or ward shall sign, adding thereto their respective residences on January first of that year, and file with the city or town clerk a sworn statement that the records and returns made by the caucus officers of such town or ward are erroneous, specifying the error, or that challenged votes were cast by persons not entitled to vote therein, said city or town clerk shall forthwith transmit such statement to the registrars of voters with the sealed package containing the ballots and voting lists, and said registrars shall give written notice to the person affected, fixing a place and time, as early as may be, at which said ballots will be recounted, and at such place and time shall open the packages containing the ballots and voting lists and recount said ballots and determine the questions raised, and shall reject any challenged vote cast by a person found not to have been entitled to vote; and such recount shall stand as the true result of the vote cast in such caucus. Each candidate affected may be present during such recount, or may be represented by an agent appointed by him in writing. If it shall appear upon a recount that persons were nominated or elected other than those declared to have been nominated or elected, certificates of such change shall be made as in the case of the original certificate.