A 270 m long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?

### Concept & Relative Speed (Opposite Direction) When two trains move in opposite directions, their relative speed is the sum of their individual speeds. The total distance they must cover to completely cross each other is the sum of their lengths. $$Relative\ Speed = S_1 + S_2$$ $$Distance = L_1 + L_2$$ ### Step-by-Step Solution 1. **Given:** Length of first train ($L_1$) = 270 m. Speed 1 = 120 kmph, Speed 2 = 80 kmph. Time = 9 s. Let the length of the second train be $L_2$. 2. Calculate the relative speed: $120 + 80 = 200$ km/hr. 3. Convert relative speed to m/s: $$200 \times \frac{5}{18} = \frac{1000}{18} = \frac{500}{9}\ m/s$$ 4. Set up the distance equation: $Distance = Speed \times Time$. $$270 + L_2 = \frac{500}{9} \times 9$$ 5. Solve for $L_2$: $$270 + L_2 = 500$$ $$L_2 = 500 - 270 = 230\ meters$$ ### Exam Strategy & Shortcut Find the relative speed (200 kmph) and convert to m/s by multiplying by $5/18$ giving $500/9$. Multiply by the time (9s) to get the total distance covered: $(500/9) \times 9 = 500$ m. Subtract the length of the first train to find the second: $500 - 270 = 230$ m. ### Common Pitfall Subtracting the speeds instead of adding them when the trains are moving in opposite directions. ### Final Answer Therefore, the correct answer is **230 m**.