Suppose the simultaneous solubility of AgCNS and AgBr in water are a and b respectively.
`{:(AgCNS hArr Ag^(+) + CNS^(-) , AgBr hArr Ag^(+) + Br^(-)),(" a a"," b b"):}`
Thus, `[Ag^(+)] = a+b , [ CNS^(-)] = a, [Br^(-) ] = b `
`K_(sp) ` of AgCNS `= [Ag^(+)] [ CNS^(-)]= a (a+b)`
`:. a(a+b) = 5 xx 10^(-12) " " ...(i)`
`K_(sp) "of" AgBr = [Ag^(+)][Br^(-)]=b (a+b)`
`:. b(a+b) = 5 xx 10^(-13) " " ...(ii)`
Dividing eqn. (i) by (ii), we get
`(a)/(b) = (10^(-12))/(5xx10^(-13))=2 or a = 2b`
Putting this value in eqn. (i)
`2b(2b+b) = 10^(-12) or 6b^(2) = 10^(-12) or b^(2) = 1/6 xx 10^(-12)`
or, `b= 4.08xx10^(-7) "mol" L^(-1) `
`a=2b=2xx4.08xx10^(-7) "mol" L^(-1) = 8.16xx10^(-7) "mol " L^(-1)`.
