$15$ kg$/$min of pure water flows into a large tank filled with $100$ kg of salt water with a mass fraction of $0\mathrm{.}2.$ In addition, the mixed solution is homogeneously mixed and then discharged from the tank at $12$ kg$/$min$.$

$(1)$What is the mass of salt water in the tank after $30$ minutes?

$(2)$What is the mass fraction of salt water in the tank after $30$ minutes?