Given information:
- The angle of elevation of the top of the tower from the point on the same level as the foot of the tower is 30 degrees.
- On advancing 150 m towards the foot of the tower, the angle of elevation becomes 60 degrees.

Goal:
To find the height of the tower.

Approach:
1. Let's assume the height of the tower is 'h' meters.
2. Draw a diagram to represent the situation.
3. Use trigonometric ratios to form equations based on the given angles and distances.
4. Solve the equations to find the value of 'h'.

Diagram:
```
T
|\
| \
| \ h
| \
| \
| \
| \
| \
| \
| \
| \
|___________\
F x P
```
- T represents the top of the tower.
- F represents the foot of the tower.
- P represents the point on the same level as the foot of the tower.
- x represents the distance from P to F.

Solution:

Step 1: Determine the equations based on the given angles and distances.
- From the given information, we can determine the following:
- tan(30°) = h / x
- tan(60°) = h / (x + 150)

Step 2: Solve the equations.
- Divide the first equation by the second equation to eliminate 'h':
- tan(30°) / tan(60°) = (h / x) / (h / (x + 150))
- 1 / √3 = x / (x + 150)
- x = (√3)(x + 150)
- √3x = (√3)(x + 150)
- √3x = √3x + 150√3
- √3x - √3x = 150√3
- 0 = 150√3
- This equation is not possible as both sides are not equal.

Step 3: Conclusion
- The equation 0 = 150√3 is not possible, which means there is an error in the given information or the problem itself. The height of the tower cannot be determined with the given data.

Therefore, the height of the tower cannot be determined as the given information is inconsistent.