In the following figure, the ratio of the areas of two sectors S1 and S2 is

Area of the sector, $S_{1}=\frac{\theta_{1}}{360} \times \pi r^{2}$

Area of the sector, $S_{2}=\frac{\theta_{2}}{360} \times \pi r^{2}$

Now we will take the ratio,

$\frac{S_{1}}{S_{2}}=\frac{\frac{\theta_{1}}{360} \times \pi r^{2}}{\frac{\theta_{2}}{360} \times \pi r^{2}}$

Now we will simplify the ratio as below,

$\frac{S_{1}}{S_{2}}=\frac{\theta_{1}}{\theta_{2}}$

Substituting the values we get,

$\frac{S_{1}}{S_{2}}=\frac{120}{150}$

$\therefore \frac{S_{1}}{S_{2}}=\frac{4}{5}$

Therefore, ratio of the areas of the two sectors is $4: 5$.

Hence, the correct answer is option $(d)$.