Here we can use the formula

$$\begin{gathered} \text{Average (A)=}\frac{\mathrm{Sum} \mathrm{of} \mathrm{observations} \left(\mathrm{S}\right)}{\mathrm{No}. \mathrm{of} \mathrm{observations} \left(\mathrm{N}\right)} \\ \text{⇒ S=A×N} \end{gathered}$$

According to the question,

Sum of weight of 35 students (A=45, N=35)

⇒S=45 X 35 =1575

Later, wieght of the teacher included, the mean weight increases by 500 g. (so A=45.5, N=36)

So, sum of 35 students and a teacher is

⇒S=45.5 X 36 =1638

Now,

The weight of the teacher is =(sum of weight of 35 students)-(Sum of wieght of 35 students and a teacher is)

=1638-1575

=63 kg.

Hence, Option A is correct.