A train traveling at 72 kmph crosses a platform in 30 seconds and a ma

Let's use some graphics to help see what's happening here.

We'll say that the train STARTS crossing the platform when the front nose of the train meets the beginning edge of the platform . . .


. . . and the train FINISHES crossing the platform when the back end of the train cross the end of the platform . . .


Let p = length of platform (in meters)
Let t = length of train (in meters)

We'll also add a blue dot at the front of train to help determine the distance the train travels.
Below, we have the train when it first meets the platform


Below, we have the train when it FINISHES crossing the platform


During this period, the total DISTANCE the train (and the blue dot) travels = p + t meters

IMPORTANT: At this point, we better convert all units to meters and seconds.

GIVEN: A train traveling at 72 kmph crosses a platform in 30 seconds
1 kilometer = 1000 meters
So, 72 kilometers per hour = 72000 meters per hour

There are 3600 seconds in an hour.
So, 72000 meters per hour = 72000 meters per 3600 seconds
= 20 meters per second [after we divide both parts by 3600]
So, the train's speed = 20 meters per second

Distance = (speed)(time)
So, if the train travels for 30 seconds at a speed of 20 meters per second, the distance traveled = (20)(30) = 600 meters

We already know that the train travels = p + t meters
So, we can write: p + t = 600

GIVEN: A train traveling at 72 kmph crosses a man standing on the platform in 18 seconds
NOTE: I'd prefer that the question asked "Which of the following BEST APPROXIMATES is the length of the platform in meters?", since the width of the man will affect the calculations.
So, let's just say the man does not have a width (width = 0)

So, here's the part where the train MEETS the man . . .


And here's the part where the train finishes PASSING the man . . .


In this case, the train travels a total distance of t meters.

Distance = (speed)(time)
So, if the train travels for 18 seconds at a speed of 20 meters per second, the distance traveled = (20)(18) = 360 meters
We already know that the DISTANCE the train travels = t meters
So, we can write: t = 360

At this point, we know that:
p + t = 600
t = 360

Subtract the bottom equation from the top equation to get: p = 240

Answer: A

Cheers,
Brent