A train crosses a stationary pole in 15 s and crosses a 100 m long platform in…

When a train crosses a stationary point object such as a pole, the distance it covers equals its own length, so its speed equals length divided by time. When the same train crosses a platform, the distance covered equals the train's length plus the platform's length.

Because the train moves at one constant speed throughout, the speed computed from the pole crossing must equal the speed computed from the platform crossing; equating the two gives an equation in the unknown train length.

1. Let the length of the train be L metres.

2. Speed from crossing the pole: L / 15.

3. Speed from crossing the platform: (L + 100) / 25.

4. Equate the two speeds: L/15 = (L + 100)/25.

5. Cross-multiply: 25L = 15(L + 100).

6. Expand and simplify: 25L = 15L + 1500, so 10L = 1500.

7. Solve: L = 150.

Check: at L = 150 m the speed is 150/15 = 10 m/s, and crossing the 100 m platform then takes (150 + 100)/10 = 25 s, exactly the time given, confirming the length. Hence the length of the train is 150 m.