the car is moving towards east with a speed of 25 km/h. To the driver of the car, a bus appears to move towards north with a speed of $25\sqrt{3}km/h$. What is the actual velocity of the bus?

The correct option is A $50km/h,{30}^o$ east of north
$V_b$= velocity of bus

$V_c$= velocity of car

$V_{bc}=25\sqrt{3}km/hr$

now from relative velocity

$|{\overrightarrow{V}}_b|$ = $\sqrt{(25{)}^2+(25\sqrt{3}{)}^2}$

= 50km/hr

for direction

$tan\theta =\frac{25\sqrt{3}}{25}=\sqrt{3}$

so ${}^{\prime }{\theta }^{\prime }$ is from east direction

Therefore it will be at 30' east of north

Hence (A) is correct