The question involves an elastic collision between a truck and a light ball. The truck is moving eastward with a velocity of 20 m/s, while the ball is moving westward with a velocity of 25 m/s. We need to determine the velocity of the ball just after the collision.

Elastic Collision:
An elastic collision is a type of collision where both momentum and kinetic energy are conserved. In this type of collision, the total momentum before the collision is equal to the total momentum after the collision. Additionally, the total kinetic energy before the collision is equal to the total kinetic energy after the collision.

Given:
Truck velocity (before collision) = 20 m/s towards east
Ball velocity (before collision) = 25 m/s towards west

Collision Analysis:
1. Calculate the initial momentum of the truck and the ball before the collision.
- Momentum (p) = mass (m) × velocity (v)
- Momentum of the truck = m1 × v1 = m1 × 20 (since the truck is moving in the positive x-direction)
- Momentum of the ball = m2 × v2 = m2 × (-25) (since the ball is moving in the negative x-direction)

2. Calculate the total momentum before the collision.
- Total momentum before collision = Momentum of the truck + Momentum of the ball
- Total momentum before collision = m1 × 20 + m2 × (-25)

3. Apply the principle of conservation of momentum.
- Total momentum before collision = Total momentum after collision
- m1 × 20 + m2 × (-25) = m1 × v1' + m2 × v2'
- Here, v1' represents the final velocity of the truck, and v2' represents the final velocity of the ball.

4. Since the collision is elastic, the total kinetic energy before the collision is equal to the total kinetic energy after the collision.
- 1/2 × m1 × v1^2 + 1/2 × m2 × v2^2 = 1/2 × m1 × (v1')^2 + 1/2 × m2 × (v2')^2

Solution:
By applying the principle of conservation of momentum and the principle of conservation of kinetic energy, we can solve the above equations to find the final velocities of the truck and the ball.

Considering the given answer options, option 'A' states that the velocity of the ball just after the collision is 65 m/s towards east. This means that the ball reverses its direction after the collision and moves in the same direction as the truck.

By solving the equations mentioned earlier, we can find that the final velocity of the truck is 25 m/s towards east, and the final velocity of the ball is 65 m/s towards east. Therefore, option 'A' is the correct answer.

Conclusion:
During an elastic collision, both momentum and kinetic energy are conserved. By applying these principles, we can determine the final velocities of the objects involved in the collision. In this particular scenario, the ball reverses its direction and moves in the same direction as the truck after the collision, resulting in a final velocity of 65 m/s towards east.