A train crosses a pole in 8 seconds. The length of the train is 120 meters. Find the time taken (in seconds) by the train to cross a platform of length 120 meters.

The correct answer is 16.

Step-by-Step Explanation:

Step 1: Understand the scenario where the train crosses a pole.
When a train crosses a stationary pole (or a person), the distance covered by the train is equal to its own length.
Given:
- Length of the train ($L$) = 120 meters
- Time taken to cross the pole ($t_1$) = 8 seconds

We can calculate the speed of the train ($v$) using the formula:
$\mathrm{Speed}=\frac{\mathrm{Distance}}{\mathrm{Time}}$

$v=\frac{120}{8}=15\text{meters/second}$

Step 2: Understand the scenario where the train crosses the platform.
When a train crosses a platform, the total distance covered by the train is the sum of the length of the train and the length of the platform.
Given:
- Length of the platform ($P$) = 120 meters
- Total distance ($D$) = Length of train + Length of platform = 120 + 120 = 240 meters

Step 3: Calculate the time taken to cross the platform.
Using the speed of the train calculated in Step 1, the time taken ($t_2$) is:
$t_2=\frac{\mathrm{Total\; Distance}}{\mathrm{Speed}}$

$t_2=\frac{240}{15}=16\text{seconds}$

Therefore, the time taken by the train to cross the platform is 16 seconds.