Two trains of equal length, each 120 metres long, take 10 seconds and 15 seconds respectively to cross a fixed post. If they are now travelling on parallel tracks in opposite directions, in how many seconds will they completely cross each other?

Introduction / Context:
This problem is another example of trains moving on parallel tracks and crossing each other. It uses the information about the times taken to pass a fixed post to deduce the speeds of the trains and then applies relative speed to find how long they take to cross each other fully when travelling in opposite directions.

Given Data / Assumptions:

• Each train has length 120 metres.
• The first train passes a post in 10 seconds.
• The second train passes a post in 15 seconds.
• Both trains move with uniform speeds on parallel tracks.
• The trains then run in opposite directions and we must find the time to cross completely.

Concept / Approach:
When a train passes a post, the distance travelled is equal to the train's own length. So from each given time we can find the speed of that train in metres per second. When the trains run in opposite directions, the relative speed is the sum of their speeds and the effective distance to be covered while crossing is the total of both lengths. Time is then found as distance divided by relative speed.

Step-by-Step Solution:
Step 1: Speed of first train = distance / time = 120 / 10 = 12 metres per second.Step 2: Speed of second train = 120 / 15 = 8 metres per second.Step 3: Relative speed when moving in opposite directions = 12 + 8 = 20 metres per second.Step 4: Total distance to be covered while crossing = 120 + 120 = 240 metres.Step 5: Time to cross each other completely = distance / speed = 240 / 20 = 12 seconds.

Verification / Alternative check:
If the trains cross in 12 seconds at relative speed 20 metres per second, the total distance covered is 20 * 12 = 240 metres.This matches the combined length of the trains (120 + 120), so the time is consistent with the given lengths and speeds.

Why Other Options Are Wrong:
The options 10 seconds or 15 seconds are simply the times taken to pass a post, not the time to cross another moving train. The option 20 seconds assumes a smaller relative speed, which is incorrect in opposite directions. The option 25 seconds would be even slower and does not match the calculated relative speed.

Common Pitfalls:
Some learners forget to add the lengths of both trains and instead use only one length, which leads to half the actual time. Others mistakenly use the difference of speeds rather than their sum, which is only appropriate when both trains move in the same direction. Clear thinking about relative motion directions is essential to avoid these missteps.

Final Answer:
The two trains will completely cross each other in 12 seconds.