Question : Two trains running in opposite directions on parallel tracks, at speeds of 42 km/hr and 57 km/hr, take 18 seconds to cross each other. If the length of one train is 270 m, then the length of the other train is:
Option 1: 250 m
Option 2: 225 m
Option 3: 230 m
Option 4: 242 m
Correct Answer: 225 m
Solution :
The relative speed of the two trains is the sum of their individual speeds, as they are moving in opposite directions.
So, the relative speed = 42 km/hr + 57 km/hr = 99 km/hr
We convert this speed into m/s multiplying by $\frac{5}{18}$.
The relative speed becomes 99 × $\frac{5}{18}$ = 27.5 m/s.
The time taken to cross each other is 18 seconds.
So, the total distance covered in this time is the sum of the lengths of the two trains.
The distance can be calculated as Speed × Time = 27.5 m/s × 18 s = 495 m
If the length of one train is 270 m, then the length of the other train is 495 m – 270 m = 225 m
Hence, the correct answer is 225 m.
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