This is the test for chloride $(Cl-)$.cidified $AgN{O}_3$ solution is added to the test solution. A white precipitate of $AgCl$, which is soluble in ammonia solution, indicates the presence of the ion.
$A{g}_{(aq)}^{+}+C{l}_{(a)p)}^{-}\to AgC{l}_{(1)}$
$AgC{l}_{(s)}+N{H}_{3(20)}\rightleftharpoons \left[Ag{\left(N{H}_3\right)}_2\right]+Cl$
Therefore, $X$ contains $Cl$.
When solution $Y$ is added to $X$, it gives a white precipitate which is soluble on boiling. This is characteristic of $PbC{l}_2$ and so $Y$ must contain $P{b}^2$