The speed of a train is 72 km/h and it crosses a platform in 25 seconds. If the train crosses an athlete whose speed is 18 km/h running in same direction of train in 10 seconds, then find the length of platform (in meters)?

To find the length of the platform, we can break the problem down into simple logical steps.

Step 1: Convert the speeds from kilometers per hour (km/h) to meters per second (m/s)
We convert speed using the conversion factor:
$1\text{km/h}=\frac{5}{18}\text{m/s}$
Speed of the train:
$V_{\text{train}}=72\times \frac{5}{18}=20\text{m/s}$
Speed of the athlete:
$V_{\text{athlete}}=18\times \frac{5}{18}=5\text{m/s}$

Step 2: Find the length of the train
When the train crosses the athlete running in the same direction, the relative speed is the difference between their speeds:
$V_{\text{relative}}=V_{\text{train}}-V_{\text{athlete}}=20-5=15\text{m/s}$
The time taken to cross the athlete is 10 seconds. The distance covered in this time is equal to the length of the train:
$\text{Length of the train}=V_{\text{relative}}\times \text{time}$
$\text{Length of the train}=15\times 10=150\text{meters}$

Step 3: Find the length of the platform
When the train crosses a stationary platform, the total distance covered is the sum of the length of the train and the length of the platform.
The time taken to cross the platform is 25 seconds.
$\text{Total distance}=V_{\text{train}}\times \text{time}$
$\text{Length of the train}+\text{Length of the platform}=20\times 25=500\text{meters}$
Substituting the length of the train:
$150+\text{Length of the platform}=500$
$\text{Length of the platform}=500-150=350\text{meters}$

Thus, the length of the platform is 350 meters.