As you may already know, the nominal agreement is the one in which the adjectives, adjective pronouns, articles, numerals and participles agree in gender and number with the head of the noun phrase they determine. However, there are some expressions that require a special note regarding their agreement, among them is "one and the other", which has the following rules:
a) When the expression "one and the other" is the subject of prayer, the singular determined (substantive) and generally the verb, although the plural is possible and preferable:
one and the other participantdeclared themselves against the measure.
one and the otherparticipantdeclared himself against the measure.
looking from one to the other side, crossed the busy avenue.
b) When the expression "one and the other" is related to names with different genders, it must agree with the male form:
They laid one of the other the girl and the dog.
Faced with embarrassment, he and she looked at each other and ended friends one of other.
By Mariana Rigonatto
Graduated in Letters
Source: Brazil School - https://brasilescola.uol.com.br/gramatica/uso-expressao-um-outro.htm