A 1   m long wire is broken into two unequal parts X and Y . The X part of the wire is stretched into…

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$R = \frac{\rho L}{A}$, where, $\rho$ is conductivity, $L$ is length of wire and $A$ is cross-sectional area of wire. For a single wire, $A$ and $\rho$ are constant. Thus, for parts $X$ and $Y$, resistance, $\frac{R_X}{R_Y} = \frac{l_X}{l_Y}$. When wire is stretched to double of its length, then resistance becomes four times, thus, $R_W = 4R_X = 2R_Y$. Hence, the ratio is $\frac{R_X}{R_Y} = \frac{1}{2}$. So, $\frac{l_X}{l_Y} = \frac{1}{2}$.