Relative Velocity in One Dimension

2025 1 question

1. Two cities X and Y are connected by a regular bus service with a bus leaving in either direction every $T\text{ min}$. A girl driving a scooty with a speed of $60\text{ km/h}$ in the direction X to Y notices that a bus goes past her every $30\text{ minutes}$ in the direction of her motion, and every $10\text{ minutes}$ in the opposite direction. Choose the correct option for the period $T$ of the bus service and the speed (assumed constant) of the buses.