A colorless aqueous solution contains nitrates of two metals, X and...

$X = {AgNO}_{3}$, $Y = Pb{\left({NO}_{3}\right)}_{2}$

$\mathop{{\text{AgNO}}_{3}}_{\left(X\right)} + \text{NaCl} \to \mathop{\text{AgCl}}_{( \text{P} )} ↓ + {\text{NaNO}}_{3}$

$\mathop{AgCl ( \text{s} ) ↓}_{( \text{P} )} + 2{\text{NH}}_{3} \to \mathop{{\left[\text{Ag}{\left({\text{NH}}_{3}\right)}_{2}\right]}^{+}}_{Soluble}{\text{Cl}}^{-}$

$\mathop{AgCl}_{( P )} + 2{Na}_{2}{S}_{2}{O}_{3} \to {Na}_{3}\mathop{\left[Ag{\left({S}_{2}{O}_{3}\right)}_{2}\right]}_{Solubel} + NaCl$

$Pb\mathop{{\left({NO}_{3}\right)}_{2}}_{\left(Y\right)} + 2NaCl \to {PbCl}_{2}$$\begin{array}{ll}Whiteppt\left(Q\right) \\ ( Solubleinhot \\ water )\end{array}$$\text{↓} + 2{NaNO}_{3}$

${\text{PbCl}}_{2}$$\begin{array}{ll}\left(aq .\right) \\ \left(Q\right)\end{array}$$+ 2\text{KI} \to \mathop{{\text{PbI}}_{2}}_{Yellowppt} + 2\text{KCl}$