Let the speed of the bus be v km/hr and the length of the bus be L meters.
When the bus passes a person moving in the same direction, the relative speed is the difference between their speeds.
For the first person moving at 3 km/hr:
Relative speed =(v−3) km/hr =(v−3)×185 m/s
Time taken =10 seconds
L=(v−3)×185×10
L=(v−3)×1850
For the second person moving at 5 km/hr:
Relative speed =(v−5) km/hr =(v−5)×185 m/s
Time taken =11 seconds
L=(v−5)×185×11
L=(v−5)×1855
Since the length of the bus is the same in both cases:
(v−3)×1850=(v−5)×1855
(v−3)×50=(v−5)×55
50v−150=55v−275
275−150=55v−50v
125=5v
v=25 km/hr
Therefore, the speed of the bus is 25 km/hr.
The answer is option 3.