When $T _1=100\,N$, Extension $=\ell_1-\ell_0$

When $T _2=120\,N$, Extension $=\ell_2-\ell_0$

Then $100= K \left(\ell_1-\ell_0\right)$

And $120= K \left(\ell_2-\ell_0\right)$

$\frac{1}{2} \Rightarrow \frac{5}{6}=\frac{\ell_1-\ell_0}{\ell_2-\ell_0}$

$5 \ell_2-5 \ell_0=6 \ell_1-6 \ell_0$

$\ell_0=6 \ell_1-5 \ell_2$

$\ell_0=6 \ell_1-5\left(\frac{11 \ell_1}{10}\right)$

$\ell_0=6 \ell_1-\frac{11 \ell_1}{2}$

$\ell_0=\frac{\ell_1}{2}$

$\therefore x=2$