A planet takes 200 days to complete one revolution around the Sun....

The Law of Periods: The square of the period of any planet is proportional to the cube of the semimajor axis of its orbit.

${T}^{2} ∝ {r}^{3}$

Therefore, we can write

${T}_{1}^{2}{r}_{1}^{3} = {T}_{2}^{2}{r}_{2}^{3}$

$⇒ \dfrac{( 200{)}^{2}}{{r}^{3}} = {T}_{2}^{2}{\left(\dfrac{r}{4}\right)}^{3}$

$⇒ \dfrac{200 \times 200}{4 \times 4 \times 4} = {T}_{2}^{2}$

$⇒ {T}_{2} = 25$ days