The length of a rubber cord is ${\ell }_1$  metres when the tension in it is 4N and ${\ell }_2$  metres when the tension is 5N. Then the length in meters when the tension is 9N is

Let $\text{'}\ell \text{'}$  be the original length and ${\ell }_3$  be the length of the wire when the tension is 9N. We know $e\propto F$ 

$\Rightarrow ({\ell }_1-\ell )\propto \mathrm{4.....}\left(1\right),$

$({\ell }_2-\ell )\propto \mathrm{5.....}\left(2\right)$

$\left({\ell }_2-\ell \right)\propto \mathrm{9.......}\left(3\right)$

From $\text{'}l\text{'}$$\left(1\right)\&\left(2\right)\frac{{\ell }_1-\ell }{{\ell }_2-\ell }=\frac{4}{5}\Rightarrow 5{\ell }_1-5\ell =4{\ell }_2-4\ell$

$\ell =5{\ell }_1-4{\ell }_2\mathrm{............}\left(4\right)$

From $\left(1\right)\&\left(3\right)\frac{{\ell }_1-\ell }{{\ell }_3-\ell }=\frac{4}{9}$    Put  is above equation and we get 

${\ell }_3=5{\ell }_2-4{\ell }_1$