A mutually agreed on number of representatives and alternates of each political party represented on the ballot by a party designation and column, appointed in the manner provided by section 16-590, may remain inside the voting area from the time the polls are closed, and, without unduly hindering or delaying the count, one representative from each party at a time may inspect the ballots, but the ballots shall at all times remain under the personal charge and keeping of the election officers and shall not be permitted to pass from their hands.