A high-speed test train $200\text{ m}$ long moving at $72\text{ km/h}$ overtakes another train $300\text{ m}$ long moving in the same direction at $36\text{ km/h}$ on parallel tracks. The time taken by the faster train to completely cross the slower train (in seconds) is:

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### 1. Strategy & Theoretical Principles When two trains travel in the same direction: - Total distance to be covered to clear each other: $D = L_1 + L_2$ - Relative speed: $V_{\text{rel}} = V_1 - V_2$ - Crossing time: $T = \frac{D}{V_{\text{rel}}}$ ### 2. Analytical Formulation & Calculation Convert speeds from $\text{km/h}$ to $\text{m/s}$: - $V_1 = 72 \times \frac{5}{18} = 20\text{ m/s}$ - $V_2 = 36 \times \frac{5}{18} = 10\text{ m/s}$ $$V_{\text{rel}} = 20 - 10 = 10\text{ m/s}$$ Total distance: $$D = 200 + 300 = 500\text{ m}$$ Time taken: $$T = \frac{500}{10} = 50\text{ seconds}$$ ### 3. Distractor Forensics - Candidate dividing by $V_1 + V_2 = 30\text{ m/s}$ calculates opposite-direction crossing ($16.67\text{ s}$). ### 4. Exam Trap & Standard Reference - **Trap Alert:** In same-direction overtaking, relative speed is the *difference*, not sum. - **Standard Reference:** Aggarwal, R.S., *Quantitative Aptitude*.

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