**Introduction:**
In this problem, we have two stones - one falling from the top of a tower and another projected vertically upwards from the ground. We need to calculate when and where these two stones will meet.

**Given data:**
- Height of the tower (h): 100 m
- Initial velocity of the stone projected upwards (u): 25 m/s
- Acceleration due to gravity (g): 9.8 m/s²

**Calculating time taken by the falling stone:**
Let's first calculate the time taken by the falling stone to reach the ground. We can use the equation of motion:

h = ut + (1/2)gt²

Substituting the given values:

100 = 0 + (1/2)(9.8)t²

Simplifying the equation:

t² = (2*100) / 9.8

t² = 20.408

t ≈ √20.408

t ≈ 4.52 seconds

Therefore, the falling stone will take approximately 4.52 seconds to reach the ground.

**Calculating the maximum height reached by the projected stone:**
Next, let's calculate the maximum height reached by the projected stone. We can use the equation of motion:

v² = u² + 2gh

At maximum height, the final velocity (v) will be zero. Substituting the given values:

0 = (25)² + 2(-9.8)h

625 = -19.6h

h ≈ -625 / -19.6

h ≈ 31.89 meters

Therefore, the projected stone will reach a maximum height of approximately 31.89 meters.

**Calculating the meeting point:**
Since both stones will be at the same height when they meet, we can equate the heights of the falling stone and the projected stone:

100 - h = h

Simplifying the equation:

2h = 100

h = 50 meters

Therefore, the two stones will meet at a height of 50 meters from the ground.

**Calculating the time taken by the projected stone to reach the meeting point:**
Now, let's calculate the time taken by the projected stone to reach the meeting point. We can use the equation of motion:

h = ut + (1/2)gt²

Substituting the given values:

50 = 25t + (1/2)(-9.8)t²

Simplifying the equation:

4.9t² + 25t - 50 = 0

Using the quadratic formula, we can solve for t:

t = (-25 ± √(25² - 4(4.9)(-50))) / (2(4.9))

t ≈ 2.04 seconds or t ≈ -4.08 seconds

Since time cannot be negative in this context, we discard the negative value.

Therefore, the projected stone will take approximately 2.04 seconds to reach the meeting point.

**Conclusion:**
The two stones will meet at a height of 50 meters from the ground after approximately 2.04 seconds.