(A):Body projected vertically up or down from the top of a tower with same velocity will reach the ground with same velocity.
(R ):Both the bodies projected vertically up and town will have same displacement and acceleration.

Answer

To solve the question, we need to analyze the statements (A) and (R) given in the problem:

**Statement (A)**: A body projected vertically up or down from the top of a tower with the same velocity will reach the ground with the same velocity.

**Statement (R)**: Both the bodies projected vertically up and down will have the same displacement and acceleration.

### Step-by-Step Solution:

1. **Understanding the Motion**:
- When a body is projected upwards, it will initially move against the gravitational force until it reaches its maximum height and then falls back down.
- When a body is projected downwards, it will move directly towards the ground under the influence of gravity.

2. **Analyzing the Final Velocity**:
- For both cases, we can use the kinematic equation:
\[ v^2 = u^2 + 2as \]
- Where:
- \( v \) = final velocity
- \( u \) = initial velocity (which is the same for both cases, denoted as \( v_0 \))
- \( a \) = acceleration (for both cases, it is \( g \) downwards)
- \( s \) = displacement (which is the height of the tower, denoted as \( h \))

3. **Applying the Kinematic Equation**:
- For the body projected upwards:
\[ v^2 = (-v_0)^2 + 2(-g)(h) \]
(Here, \( -g \) is used because the acceleration is directed downwards.)
- For the body projected downwards:
\[ v^2 = v_0^2 + 2gh \]

4. **Final Velocity Calculation**:
- In both cases, when we calculate the final velocity just before hitting the ground, we will find that:
\[ v^2 = v_0^2 + 2gh \]
- The final velocity \( v \) will be the same in magnitude for both cases, but the direction will be opposite (downwards).

5. **Displacement and Acceleration**:
- Both bodies travel the same vertical distance \( h \) (the height of the tower).
- The acceleration due to gravity \( g \) is the same for both bodies.

6. **Conclusion**:
- Thus, both statements (A) and (R) are true. Statement (R) correctly explains statement (A) because both bodies experience the same displacement and acceleration, leading to the same final velocity.

### Final Answer:
- **(A)** is true.
- **(R)** is true and correctly explains (A).