JEE Chemistry Practice Question

At $298 \mathrm{~K}$, the limiting molar conductivity of a weak monobasic acid is $4 \times 10^2 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$. At $298 \mathrm{~K}$, for an aqueous solution of the acid the degree of dissociation is $\alpha$ and the molar conductivity is $\mathbf{y} \times 10^2 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$. At $298 \mathrm{~K}$, upon 20 times dilution with water, the molar conductivity of the solution becomes $3 \mathbf{y} \times 10^2 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$. What is the value of $\alpha$?