Amendments to any charter adopted by the City of Baltimore or by any County of this State under the provisions of this Article may be proposed by a resolution of the Mayor of Baltimore and the City Council of the City of Baltimore, or the Council of the County, or by a petition signed by not less than 20% of the registered voters of the City or County, provided, however, that in any case 10,000 signatures shall be sufficient to complete a petition. A petition shall be filed with the Mayor of Baltimore or the President of the County Council. An amendment so proposed shall be submitted to the voters of the City or County at the next general or congressional election occurring after the passage of the resolution or the filing of the petition. If at the election the majority of the votes cast for and against the amendment shall be in favor thereof, the amendment shall be adopted and become a part of the charter of the City or County from and after the thirtieth day after said election. The amendments shall be published by the Mayor of Baltimore or President of the County Council once a week for five successive weeks prior to the election in at least one newspaper published in said City or County.