The distance between Sun and Earth is $R$. The duration of year if the distance between Sun and Earth becomes $3R$ will be :

According to Kepler's Third Law – The Law of Periods,

$\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }\mathrm{ }{T}^2\propto R^3$

where $T$ is time taken by the planet to go once around the sun and $R$ is the semi-major axis (distance) of the elliptical orbit.

$\therefore T^2={k R}^3 \dots$(i)

Where $k$ is a constant of proportionality.

When $R$ becomes $3$ times, let the time period be $\left(T^{\text{'}}\right)$.

$\therefore {\left(T^{\text{'}}\right)}^2=k(3R{)}^3 \dots (\mathrm{i}\mathrm{i})$

$\therefore \frac{T^2}{{\left(T^{\text{'}}\right)}^2}=\frac{1}{27}$

So, time period will be $3\sqrt{3} \mathrm{yr}$.