A train is running at a speed of 72 km/hr and crosses a platform in 20 sec and a pole in 14 second. Find the length of the platform (in meter).

The correct answer is 120.

Step-by-step Explanation:

Step 1: Convert the speed of the train from km/hr to m/s
The speed of the train is given as 72 km/hr. Since the time is in seconds and we need the length in meters, we first convert the speed into meters per second (m/s).
To convert from km/hr to m/s, we multiply by $\frac{5}{18}$.

$\text{Speed}=72\times \frac{5}{18}=4\times 5=20\text{m/s}$

Step 2: Understand what happens when the train crosses a pole
When a train crosses a stationary pole (or any point object of negligible length), the distance traveled by the train is equal to its own length.
Let the length of the train be $L$ meters.
The train crosses the pole in 14 seconds at a speed of 20 m/s.

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

$L=20\text{m/s}\times 14\text{s}=280\text{meters}$

So, the length of the train is 280 meters.

Step 3: Understand what happens when the train crosses a platform
When a train crosses a platform of length $P$ meters, the total distance traveled by the train is the sum of the length of the train and the length of the platform.
$\text{Total Distance}=L+P$
The train crosses the platform in 20 seconds.

$\text{Total Distance}=\text{Speed}\times \text{Time}$

$L+P=20\text{m/s}\times 20\text{s}$

$280+P=400$

Step 4: Solve for the length of the platform (P)

$P=400-280=120\text{meters}$

Therefore, the length of the platform is 120 meters.