In 1 ~L saturated solution of AgCl[K_ sp AgCl=1.6 × 10^ -10 ], 0.1...

It is a case of simultaneous solubility of salts with a common ion. Here solubility product of $\mathrm{CuCl}$ is much greater than that of $\mathrm{AgCl}$, it can be assumed that $\mathrm{Cl}^{-}$in solution comes mainly from $\mathrm{CuCl}$. \Rightarrow \quad$\left[\mathrm{Cl}^{-}\right]=\sqrt{K_{s p}(\mathrm{CuCl})}=$10^{-3} $\mathrm{M}$Now for $\mathrm{AgCl}: K_{s p}=1.6 \times 10^{-10}=\left[\mathrm{Ag}^{+}\right]\left[\mathrm{Cl}^{-}\right]=\left[\mathrm{Ag}^{+}\right] \times 10^{-3} \Rightarrow\left[\mathrm{Ag}^{+}\right]=1.6 \times 10^{-7}$