Why do resistant bacteria multiply faster after a patient has taken antibiotics compared to a healthy person who has not taken antibiotics?

When patient takes in antibiotics the resistance bacteria gets a competitive survival advantage over the normal sensitive bacteria and hence grows faster.

Explanation:

Bacteria can acquire resistance by taking in plasmids containing MDR (Multi-Drug Resistance) gene cassettes. The MDR genes produces proteins that can:Render the antibiotic ineffective to act on its target by inducing chemical modifications on the drug.Promote efflux of the drug from the bacterial cell so that the drug cannot act upon its target.When a healthy person ( having no prior exposure to the antibiotic) is infected by bacteria ( both sensitive and resistant varieties):A competition develops for the host cells and nutrients between the sensitive and the resistant variety.This mutual competition restricts either of the sensitive or resistant bacterial strain to grow profusely.When a person (having prior antibiotic exposure), gets infected by bacteria ( both sensitive and resistant varieties) and is exposed to the same antibiotic:The sensitive variety, due to its sensitivity towards the drug, gets killed.The resistant variety, due to its MDR genes, bypasses the lethal effect of the drug and survives.These surviving resistant bacteria can now infect all the available host cells and utilise all the available nutrients without facing any competition and multiply rapidly.