Understanding the Problem
The problem states that a train overtakes two persons walking at speeds of 8kmph and 12kmph respectively. The train completely passes the two persons in 9 seconds and 10 seconds respectively. We need to find the length of the train.

Key Information
- Speed of first person = 8 kmph
- Speed of second person = 12 kmph
- Time taken to pass both persons = 9 seconds and 10 seconds
- We need to find the length of the train

Solution

Step 1: Calculate Relative Speed of Train
- Relative speed of the train with respect to the first person = Speed of train - Speed of first person = x - 8 kmph
- Relative speed of the train with respect to the second person = Speed of train - Speed of second person = x - 12 kmph

Step 2: Calculate Length of Train
- Distance covered by the train while passing the first person = Speed * Time = (x - 8) * 9 meters
- Distance covered by the train while passing the second person = (x - 12) * 10 meters
- Total distance covered by the train to cross both persons = Length of the train

Step 3: Set up the Equation
- (x - 8) * 9 + (x - 12) * 10 = Length of the train

Step 4: Solve the Equation
- Simplify the equation to find the value of x
- Once x is calculated, substitute it back to find the length of the train

Step 5: Final Answer
- The length of the train can be calculated using the value of x obtained in the previous step
By following these steps, you can determine the length of the train based on the given information.

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