Two trains are moving in the same direction at 60 km/h and 42 km/h. The faster train crosses a man in the slower train in 36 seconds. Find the length of the faster train.

The correct option is 180 m.

To find the length of the faster train, we can use the concept of relative speed since both trains are moving in the same direction.

Step 1: Determine the relative speed of the trains
When two objects move in the same direction, their relative speed is the difference between their individual speeds.
Given:
Speed of the faster train = 60 km/h
Speed of the slower train = 42 km/h
Therefore, the relative speed ($v$) is:
$v=60-42=18\text{ km/h}$

Step 2: Convert the relative speed into meters per second (m/s)
Since the time is given in seconds and the options are in meters, we convert the speed from km/h to m/s by multiplying by $\frac{5}{18}$:
$v=18\times \frac{5}{18}=5\text{ m/s}$

Step 3: Calculate the length of the faster train
The faster train crosses a man sitting in the slower train. In this scenario, the distance covered to cross the man is equal to the length of the faster train ($L$).
Using the formula:
$\text{Distance}=\text{Speed}\times \text{Time}$
Given that the time taken to cross the man is 36 seconds:
$L=5\text{ m/s}\times 36\text{ s}=180\text{ m}$

Thus, the length of the faster train is 180 m.