Bacterial populations can develop drug resistance in a short time by self –transferable plasmids. Few of them carries antibiotic resistance genes for metabolic functions. The overdose of antibiotics for people with a cold increases the killing of the healthy bacteria.
Bacteria can develop resistance in the following ways.
Mutation: By cell replication, some bacteria develop mutations that makes them resistant to antibiotics. Bacteria with the resistant mutation can survive against antibiotics. These resistant bacteria continue to multiply  even when they are exposed to antibiotics
Horizontal Gene Transfer: Antibiotic-resistant genetic material is transferred between different bacteria cells in three different ways: transformation, transduction or conjugation.