Capacitance of isolated conducting sphere C=4πϵ0R1
By enclosing inside another sphere of radius R2, new capacitance C′=(R2−R1)4πϵ0R1R2
Given: (R2−R1)4πϵ0R1R2=n×4πϵ0R1
⇒(R2−R1)R2=n⇒(R1R2−1)R1R2=n
⇒R1R2=nR1R2−n⇒R1R2=(n−1)n