b
$\frac{ R _{ X }}{ R _{ Y }}=\frac{\ell_{ X }}{\ell_{ Y }}$
When wire is stretched to double of its length, then resistance becomes 4 times
$R _{ W }=4 R _{ X }=2 R _{ Y }$
$\frac{ R _{ X }}{ R _{ Y }}=\frac{1}{2}$
So. $\frac{\ell_{ X }}{\ell_{ y }}=\frac{1}{2}$