Initially, $\frac{P}{Q}=\frac{40 \mathrm{~cm}}{60 \mathrm{~cm}}=\frac{2}{3}$ Finally, $\frac{P+x}{Q}=\frac{80 \mathrm{~cm}}{20 \mathrm{~cm}}=\frac{4}{1}$ Divide (2) by (1) $$ \begin{aligned} & \frac{P+x}{Q}=4 \times \frac{3}{2}=6 \quad \Rightarrow 1+\frac{x}{P}=6 \Rightarrow \frac{x}{P}=5 \\ & \therefore x=5 P=5 \times 4=20 \Omega \end{aligned} $$