Given Information:
- Two trains cross each other in 145 seconds when moving in the same direction.
- They cross each other in 29 seconds when running in opposite directions.
- Length of the first train is 600 meters.
- Length of the second train is 850 meters.

To find:
- The speed of the slower train in km/hr.

Let's break down the solution into steps:

Step 1: Find the relative speed of the trains when moving in the same direction
- When the trains are moving in the same direction, their relative speed is the difference of their individual speeds.
- Let the speed of the slower train be x km/hr.
- So, the speed of the faster train would be (x + y) km/hr, where y is the additional speed of the faster train.
- The relative speed of the trains, when moving in the same direction, is (x + y) - x = y km/hr.

Step 2: Calculate the relative speed of the trains when running in opposite directions
- When the trains are running in opposite directions, their relative speed is the sum of their individual speeds.
- So, the relative speed of the trains, when running in opposite directions, is (x + y) + x = 2x + y km/hr.

Step 3: Calculate the time taken to cross each other in both scenarios
- When the trains are moving in the same direction, they cross each other in 145 seconds.
- So, the time taken to cross each other when moving in the same direction is the total distance covered (600 + 850) meters divided by the relative speed of the trains.
- Therefore, 145 = (600 + 850) / y

- Similarly, when the trains are running in opposite directions, they cross each other in 29 seconds.
- So, the time taken to cross each other when running in opposite directions is the total distance covered (600 + 850) meters divided by the relative speed of the trains.
- Therefore, 29 = (600 + 850) / (2x + y)

Step 4: Solve the equations to find the values of x and y
- We have two equations and two variables, y and x.
- Solve the equations simultaneously to find the values of x and y.

By solving the equations, we get y = 12 m/s and x = 20 m/s.

Step 5: Convert the speed to km/hr
- The speed of the slower train is x km/hr.
- Therefore, the speed of the slower train is 20 km/hr.

Hence, the correct answer is option 'A' (72 km/hr).