Given
Total number of students in school $$ = 4050 $$
Student –teacher ratio in a school $$ = 45: 2 $$
Let us assume that the total number of teachers in school be $$x$$
Hence,
Required ratio = Total number of students / Total number of teachers
We get
$$ 45 : 2 = 4050 : x $$
$$ \dfrac{45}{2} = \dfrac{4050}{x} $$
$$ x = \dfrac{4050 \times 2}{45} $$
$$ x = \dfrac{8100}{45} $$
$$ x = 180 $$ teachers