Relative velocity

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.

The speed of a swimmer in still water is 20 m/s. The speed of river water is 10 m/s and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes w.r.t. north is given by :

Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time \(t_1\). On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time \(t_2\). The time taken by her to walk up on the moving escalator will be :