Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is (S.S.C., 2003)

### Concept & Equal Speeds in Opposite Directions When two identical objects move toward each other at the same speed, the relative speed is twice the speed of one object. The distance covered to cross is the sum of their lengths. $$Relative\ Speed = 2v$$ $$Total\ Distance = 2L$$ ### Step-by-Step Solution 1. **Given:** Length of each train = 120 m. Total distance = $120 + 120 = 240$ m. Time = 12 s. Let the speed of each train be $v$ m/s. 2. The relative speed since they are in opposite directions is $v + v = 2v$. 3. Calculate relative speed using distance and time: $$Relative\ Speed = \frac{Distance}{Time} = \frac{240}{12} = 20\ m/s$$ 4. Set the equations equal to find the speed of one train: $$2v = 20 \implies v = 10\ m/s$$ 5. Convert the speed from m/s to km/hr: $$10 \times \frac{18}{5} = 36\ km/hr$$ ### Exam Strategy & Shortcut Total distance is 240m. Time is 12s. Combined speed = $240/12 = 20$ m/s. Since speeds are equal, one train's speed is 10 m/s. Multiply by $18/5$ to get 36 km/hr instantly. ### Common Pitfall Stopping the calculation at the relative speed (20 m/s or 72 km/hr) and choosing that as the answer, forgetting that it represents the *combined* speed of both trains. ### Final Answer Therefore, the correct answer is **36**.