Consider a mixture $X$ which is made by dissolving $0.4$ mol of $[\mathrm{Co(NH_3)_5SO_4}]Br$ and $0.4$ mol of $[\mathrm{Co(NH_3)_5Br}]SO_4$ in water to make $4$ L of solution. When $2$ L of mixture $X$ is allowed to react with excess $\mathrm{AgNO_3}$, it forms precipitate $Y$. The rest $2$ L of mixture $X$ reacts with excess $\mathrm{BaCl_2}$ to form precipitate $Z$. Which of the following statements is CORRECT?