Train A travelling at 63 kmph can cross a platform 199.5 m long in 21 seconds. How much time would train A take to completely cross (from the moment they meet) train B, 157m long and travelling at 54 kmph in opposite direction which train A is travelling? (in seconds) [IBPS—RRB Office Assistant (Online) Exam, 2015]

### Concept & Logic First, find the length of Train A using its speed and time taken to cross the platform. Then, calculate the relative speed of both trains moving in opposite directions to find the total crossing time. $$ \text{Time} = \frac{\text{Length of A} + \text{Length of B}}{\text{Speed of A} + \text{Speed of B}} $$ ### Step-by-Step Solution 1. **Convert Speed of Train A:** - Speed of A = $63$ kmph = $63 \times \frac{5}{18} = \frac{35}{2} = 17.5$ m/s. 2. **Find Length of Train A ($L_A$):** - Total distance in 21 seconds = $17.5 \times 21 = 367.5$ m. - $L_A + 199.5 = 367.5 \Rightarrow L_A = 168$ m. 3. **Calculate Relative Speed:** - Speed of B = $54$ kmph = $54 \times \frac{5}{18} = 15$ m/s. - Relative speed = $17.5 + 15 = 32.5$ m/s. 4. **Find Crossing Time:** - Total distance = $L_A + L_B = 168 + 157 = 325$ m. - Time = $\frac{325}{32.5} = 10$ seconds. ### Exam Strategy & Shortcut Convert all speeds cleanly into decimals or fractions (e.g., $17.5$ and $15$) to make relative speed addition ($32.5$) and division with $325$ exceptionally straightforward without calculator reliance. ### Common Pitfall Forgetting to add the two train lengths together when crossing each other, or mixing up the relative speed signs for opposite directions. ### Final Answer Therefore, the correct answer is **10**.