A train 200 metres long is moving at the rate of 40 kmph. In how many seconds will it cross a man standing near the railway line ?

The correct answer is 18 seconds.

When a train crosses a man (or a stationary point) standing near the railway line, the total distance the train must cover is equal to its own length. This is because the train is said to have "crossed" the man only after the entire train — from its front to its rear — has passed him.

Step 1: Identify the given information

Length of train = 200 metres
Speed of train = 40 km/h
Distance to be covered = 200 metres (equal to the length of the train)

Step 2: Convert speed from km/h to m/s

To match our distance unit (metres), we must convert the speed from kilometres per hour to metres per second using the standard conversion factor:

$1\text{km/h}=\frac{5}{18}\text{m/s}$

So, speed in m/s:

$40\times \frac{5}{18}=\frac{200}{18}=\frac{100}{9}\text{m/s}$

Step 3: Apply the Time-Speed-Distance formula

$\text{Time}=\frac{\text{Distance}}{\text{Speed}}$

Substituting the values:

$\text{Time}=\frac{200}{\frac{100}{9}}=200\times \frac{9}{100}=\frac{1800}{100}=18\text{seconds}$

Conclusion: The train will cross the man standing near the railway line in 18 seconds.