$\frac{P}{Q}=\frac{\ell_{1}}{100-\ell_{1}}$

$\ell_{1}=55 \mathrm{\,cm}$

or $\quad 100-\ell_{1}=45 \mathrm{\,cm}$

$\because $ $\mathrm{P}=3\, \Omega$

or $\mathrm{Q}=3 \times \frac{45}{55}=3 \times \frac{9}{11}=\frac{27}{11}\, \Omega$

when $\mathrm{x}$ is connected in series with $P, \ell_{1}=75 \mathrm{\,cm}$

or  $\frac{\mathrm{P}+\mathrm{x}}{\mathrm{Q}}=\frac{75 \mathrm{\,cm}}{25 \mathrm{\,cm}}$

$3+x=3 \times \frac{27}{11}$

$\mathrm{x}=\frac{81}{11}-3$ or $\quad x=\frac{48}{11} \,\Omega$