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 option is 120.

Here is the step-by-step explanation to find the length of the platform:

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. To convert this speed into meters per second (m/s), we multiply it by $\frac{5}{18}$:
$\text{Speed}=72\times \frac{5}{18}=20\text{ m/s}$
So, the speed of the train is 20 m/s.

Step 2: Find the length of the train
When a train crosses a pole, it covers a distance equal to its own length. Let the length of the train be $L$.
The train takes 14 seconds to cross the pole. Using the formula $\text{Distance}=\text{Speed}\times \text{Time}$:
$L=20\text{ m/s}\times 14\text{ s}=280\text{ meters}$
Thus, the length of the train is 280 meters.

Step 3: Find the length of the platform
When the train crosses a platform, the total distance covered is the sum of the length of the train ($L$) and the length of the platform ($P$).
The train takes 20 seconds to cross the platform. Using the distance formula:
$L+P=\text{Speed}\times \text{Time}$
$L+P=20\text{ m/s}\times 20\text{ s}=400\text{ meters}$
Now, substitute the value of $L=280$ meters into the equation:
$280+P=400$
$P=400-280=120\text{ meters}$
Therefore, the length of the platform is 120 meters.