Question : Two trains of the same length are running on parallel tracks in the same direction at the speeds of 60 km/h and 90 km/h, respectively. The latter completely crosses the former in 30 seconds. The length of each train (in meters) is:
Option 1: 125
Option 2: 150
Option 3: 100
Option 4: 115
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Correct Answer: 125
Solution :
Time taken to cross each other = $\frac{\text{Sum of the lengths of two trains}}{\text{Relative speed}}$
Let the length of each train be $x$ meters.
So, total length = $2x$ meters.
Speed of 1st train = 30 km/h
Speed of 2nd train = 45 km/h
Relative speed = 45 – 30 = 15 km/h
Converting this into m/sec,
⇒ $\frac{5}{18}×15=\frac{25}{6}$ m/sec.
Time taken by the 2nd train to cross the 1st train completely = 60 seconds.
Total length = time × relative speed.
⇒ $2x=60×\frac{25}{6}$
⇒ $x=5×25$ = 125 meters.
Hence, the correct answer is 125.
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