Problem Analysis

We need to find the length of the train ($L$) given two scenarios:

• The train crosses a man (point object) in 10 seconds.
• The train crosses a platform of 260 m in 20 seconds.

Let the speed of the train be $S$ m/s.

Calculating Train Speed and Length

Scenario 1: Crossing a man
When a train crosses a man, the distance covered is equal to the length of the train ($L$).
Time = Distance / Speed
$10 = L / S$
From this, we get the relation: $L = 10S$ (Equation 1)

Scenario 2: Crossing a platform
When a train crosses a platform, the total distance covered is the length of the train ($L$) plus the length of the platform (260 m).
Time = Total Distance / Speed
$20 = (L + 260) / S$
This gives us: $20S = L + 260$ (Equation 2)

Solving for Length ($L$)
Substitute the value of $L$ from Equation 1 into Equation 2:
$20S = (10S) + 260$
Subtract $10S$ from both sides:
$20S - 10S = 260$
$10S = 260$
Calculate the speed $S$:
$S = 260 / 10$
$S = 26$ m/s

Now, substitute the speed $S$ back into Equation 1 to find the length $L$:
$L = 10S$
$L = 10 \times 26$
$L = 260$ m

Conclusion

The length of the train is 260 meters.