To calculate the time taken by the train to cross a person, we use the formula:

Distance Travelled by the Train = Length of the Train

Given:

• Length of the train = $200$ meters
• Speed of the train = $40$ km/h

Now, convert the speed into meters per second: $1$ km/h = $\frac{1000}{3600}$ meters per second, so: Speed of the train = $40 imes \frac{1000}{3600}$ meters per second

Now, using the formula:

Time = Distance / Speed

Substitute the values:

• Distance = $200$ meters
• Speed = $40 imes \frac{1000}{3600}$ meters per second

So, the time taken to cross the person:

Time = $\frac{200}{40 imes \frac{1000}{3600}}$

Simplifying:

Time = $200 imes \frac{3600}{40 imes 1000}$

Time = $\frac{720000}{40000} = 18$ seconds

Thus, the train will take $18$ seconds to cross the person.