Initial balance at 40 cm: R2R1=6040=32 ...(i)
With 16Ω parallel to R2, null point at 50 cm:
16+R216R2R1=5050=1⇒R1=16+R216R2 ...(ii)
From (i): R1=32R2.
Substituting in (ii): 32R2=16+R216R2.
32=16+R216⇒2(16+R2)=48⇒R2=8Ω.
R1=316Ω.