The distance from Patna to Ranchi is 260 km by air and 320 km by...

The average velocity is defined as the ratio of total displacement to the total time taken.

The displacement of the bus is the shortest straight-line distance between the initial and final positions, which is equal to the distance by air.

Displacement $= 260 \text{ km}$

The direction of displacement is from Patna to Ranchi.

Time taken by the bus $= 8 \text{ h}$

Average velocity $= \dfrac{\text{Displacement}}{\text{Time}} = \dfrac{260}{8} = 32.5 \text{ km/h}$

The direction of the average velocity is the same as the direction of displacement, which is from Patna to Ranchi.