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By Kepler's law

$T^2 \;\alpha \; a^3$

$\large\frac{T_1^2}{a_1 ^3}=\frac{T_2^2}{a_2^3}$

$ T_2^2 =\bigg( \large\frac{a_2}{a_1}\bigg)^3 $$ \times T_1^2$

$ T_2^2 =\bigg( \large\frac{1}{2}\bigg)^3 $$ \times T_1^2$

$ T_2^2 =\bigg( \large\frac{1}{8}\bigg) $$ \times 1\;year$

$ T_2 =\large\frac{1}{\sqrt 8} $$ \times 365\;days$

$\quad=129\;days$

Hence b is the correct answer.

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