Let [Ag] and [SO_{4}] be the initial concentration of the 2 ions in the various solutions.

Let the amount of AgNO_{3} solution added be Xml

When combined, [tex][Ag]new= \frac{x[Ag]}{x+10}[/tex], [tex][SO_4]new= \frac{10[SO_4]}{x+10}[/tex]

Thus, [tex]Ksp = \frac{10x^2[Ag]^2[SO_4]}{(x+10)^3}[/tex]

[Ag]^{2}[SO4]=1.2x10^{-5} (Actually specific value doesn't matter)

Sub this into the Ksp equation, then max X is when [tex]\frac{d}{dx} \frac{10x^2×1.2×10^{-5} }{(x+10)^3}=0[/tex]

Solving, X=20.