A scooter and its rider, having a combined mass of 150 kg , are...

Given:
Mass $m = 150 \text{ kg}$
Velocity $v = 36 \text{ km/hr} = 36 \times \dfrac{5}{18} \text{ m/s} = 10 \text{ m/s}$
Radius $r = 30 \text{ m}$
Acceleration due to gravity $g = 10 \text{ m/s}^2$

For banking without friction, the necessary centripetal force is provided entirely by the horizontal component of the normal reaction.

$N \sin \theta = \dfrac{mv^2}{r}$

$N \cos \theta = mg$

Dividing the two equations:

$\tan \theta = \dfrac{v^2}{rg}$

Substituting the given values:

$\tan \theta = \dfrac{(10)^2}{30 \times 10}$

$\tan \theta = \dfrac{100}{300} = \dfrac{1}{3}$

$\theta = \tan^{-1} \left(\dfrac{1}{3}\right)