The city collector shall report to the city council, at the regular meetings in each month, all taxes collected on the real and personal delinquent lists; and he shall pay the same to the city treasurer, and receive credit therefor. He shall turn over to his successor all uncollected delinquent lists, receiving credit therefor, and his successor shall be charged therewith; provided, that the city council may declare worthless any and all personal delinquent taxes which the council may deem uncollectible.