Mealworms typically lay there eggs in foods such as cereal or other foods that are made of grain.
So make sure to keep your cereal or other grain based foods stored in sealed containers to keep the mealworms out of it.
I've had mealworms lay their eggs in some cereal that I had in a box on my counter and I only noticed it after I poured the cereal in the bowl and almost ate it.
So now I keep my cereal and other foods such as oatmeal etc in sealed containers inside my cabinets.
It takes around 2 weeks for the adult mealworm beetle to mate and lay it's eggs after it emerges from the Pupa or Cocoon.
Every Female Mealworm beetle can lay up to 100 to 200 eggs at one time and can lay up to 500 eggs in it's life.
The mealworm beetle can live from 2 months to as long as 15 years.