Two cities X and Y are connected by a regular bus service with a bus leaving in either direction every $T$ min. A girl is driving scooty with a speed of 60 km/h in the direction X to Y notices that a bus goes past her every 30 minutes in the direction of her motion, and every 10 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.
$\dfrac{vT}{v-60} = 30$, $\dfrac{vT}{v+60} = 10$. Dividing: $\dfrac{v+60}{v-60} = 3\Rightarrow v = 120$ km/h; then $T = 15$ min.