Option 4 : 225 km/hr.

Given:

If it runs at a speed of 150 km/hr on an average,

then, time is 3 hours.

Formula used:

Speed = Distance/Time

Distance = Speed × Time

Calculation:

According to the question:

Distance = Speed × Time

⇒ Distance = 150 × 3 = 450 km

Now, new time will be 2 hours, then

Speed = Distance/Time

⇒ Speed = 450/2 = 225 km/hr.

∴ The speed of the train is 225 km/hr.

__Hint__

1. We are having time and speed given, so first we will calculate the distance. Then we can get new speed for given time and distance.

2. Find distance covered in both case using formula Distance = Speed × Time

As distance is same in both cases, you should equate distance to get the value of new speed.

__Additional Information__

Distance covered = Speed × Time

- Units of Time, Speed and Distance
- The basic unit of time is a second, which could also be expressed in other units such as minutes (min) and hours (hr).
- The basic unit of speed is meter per second m/s, which could also be expressed in other units such as m/min or km/h.
- The basic unit of distance meter (m), which could also be expressed in other units such as kilometre (km).
- To convert a speed given in m/s into a speed in km/h, multiply with 18/5.
- To convert a speed given in km/h into a speed in m/s, multiply with 5/18.
- 1 km = 1000 m
- 1 min = 60 sec.

Average speed:

- 1. When a body travels different distances at different speeds, the average speed is the amount of time taken to travel the total distance in total time, Therefore, the formula for Time Speed Distance is:
- Average speed = Total distance/ Total time
- 2. When the body travels at speeds of u and v units for equal distances:
- Average speed = 2uv/(u + v)

Relative speed:

- Consider two bodies moving at speeds u and v.
- 1. When they are moving in the same direction, the relative speed between the two bodies is the difference of their speeds,
- (u – v) if u > v
- (v – u) if v > u.
- 2. When they are moving in the opposite directions, the relative speed between the two bodies is the sum of their speeds,
- (u + v).