Two trains, 140 metres and 160 metres long respectively, run on parallel tracks in opposite directions. Their speeds are 60 km/h and 40 km/h respectively. How many seconds will they take to completely cross each other?

Introduction / Context:
This problem again checks understanding of relative speed when two trains move in opposite directions. The twist is that the two trains have different lengths and different speeds. The key skills tested are unit conversion and correctly determining the total distance and relative speed.

Given Data / Assumptions:

• Length of first train = 140 metres.
• Length of second train = 160 metres.
• Speed of first train = 60 km/h.
• Speed of second train = 40 km/h.
• The trains move in opposite directions on parallel tracks.
• We must find the time taken for them to completely cross each other.

Concept / Approach:
When trains move in opposite directions, the total distance to be covered to cross completely is the sum of their lengths. Their relative speed is the sum of their individual speeds. We convert the speeds from km/h to metres per second, add them to get the relative speed, then divide the total distance by this relative speed to obtain the required crossing time in seconds.

Step-by-Step Solution:
Step 1: Total distance to be covered while crossing = 140 + 160 = 300 metres.Step 2: Convert speeds to metres per second: 60 km/h = 60 * 5 / 18 = 50 / 3 metres per second.Step 3: Similarly, 40 km/h = 40 * 5 / 18 = 100 / 9 metres per second.Step 4: Relative speed in opposite directions = 50 / 3 + 100 / 9 = (150 + 100) / 9 = 250 / 9 metres per second.Step 5: Time = distance / speed = 300 / (250 / 9) = 300 * 9 / 250 = 2700 / 250 = 10.8 seconds.

Verification / Alternative check:
We can approximate: 60 km/h and 40 km/h sum to 100 km/h, roughly equal to 27.78 metres per second.Then time ≈ 300 / 27.78 ≈ 10.8 seconds, consistent with the exact calculation.

Why Other Options Are Wrong:
Values like 9 seconds or 9.6 seconds are too short and correspond to a higher relative speed than possible with 60 km/h and 40 km/h. The options 10 seconds or 12 seconds are rough guesses that do not match the exact ratio of distance to relative speed when recalculated precisely.

Common Pitfalls:
One common error is to forget to add the lengths of both trains and use only a single length as the total distance. Another is to use the difference of speeds instead of the sum when trains move in opposite directions. Also, some students forget to convert from km/h to metres per second, which leads to inconsistent units and wrong times.

Final Answer:
The trains will completely cross each other in 10.8 seconds.