Two train drivers Santhosh and Rekha are both in the engine of a train of length 60 meters.  As the train enters a platform, Rekha walks at a uniform speed inside the train toward the guard compartment in the rear.  She picks up her handbag from the guard compartment and walks back at the same speed in the train towards the engine and reaches Santhosh after 40 seconds. When she meets Santhosh she tells him that she took 12 seconds to pass the platform.  But Santhosh says that he only took 8 seconds to pass the platform.  Find the length of the platform.

To solve this problem, we need to understand that the speed of the train is constant and that the speed of Rekha walking inside the train is also constant.

1. First, let's find the speed of the train. We know that the train took 8 seconds to pass the platform. The length of the train is 60 meters. So, the speed of the train is 60 meters / 8 seconds = 7.5 meters/second.

2. Now, let's find the distance Rekha walked inside the train. We know that she walked for 40 seconds at a constant speed. Since the speed of the train is 7.5 meters/second, the distance she walked is 7.5 meters/second * 40 seconds = 300 meters.

3. However, this distance includes the length of the train twice (once when she walked to the guard compartment and once when she walked back). So, the actual distance she walked inside the train is 300 meters - 2*60 meters = 180 meters.

4. Now, let's find the speed of Rekha. We know that she took 12 seconds to pass the platform. So, her speed is (length of the train + length of the platform) / 12 seconds.

5. We also know that her speed is (length of the train + distance she walked inside the train) / 40 seconds. So, we can set these two expressions equal to each other and solve for the length of the platform.

(length of the train + length of the platform) / 12 seconds = (length of the train + distance she walked inside the train) / 40 seconds

Solving this equation gives us the length of the platform = 120 meters.