Two trains start from stations $A$ and $B$ and travel towards each other at a speed of 50 kmph and 60 kmph respectively. A the time of their meeting, the second train had travelled 120 km more than the first. The distance between $A$ and $B$ is

### Concept & Speed Difference When two objects move towards each other for the same duration, the difference in the distance they cover is simply their relative speed difference multiplied by the total time traveled. $$Distance\ Difference = (Speed_2 - Speed_1) \times Time$$ ### Step-by-Step Solution 1. **Identify the speeds:** Train 1 speed = 50 km/hr, Train 2 speed = 60 km/hr. 2. **Find the difference in speed:** $$Speed\ Difference = 60 - 50 = 10 \text{ km/hr}$$ This means for every hour they travel, the second train covers 10 km more than the first. 3. **Find the time to meet:** The total extra distance covered by the second train is 120 km. $$Time = \frac{Extra\ Distance}{Speed\ Difference}$$ $$Time = \frac{120}{10} = 12 \text{ hours}$$ They traveled for 12 hours before meeting. 4. **Calculate total distance:** The total distance is the sum of their individual speeds (relative speed towards each other) multiplied by the total time. $$Total\ Distance = (50 + 60) \times 12$$ $$Total\ Distance = 110 \times 12 = 1320 \text{ km}$$ ### Exam Strategy & Shortcut Think of it logically: The faster train gains 10 km on the slower train every hour. To gain 120 km, it must have been traveling for 12 hours. In 1 hour, together they cover 110 km. In 12 hours, they cover $110 \times 12 = 1320$ km. ### Common Pitfall Assuming 120 is the relative distance to solve for time using the sum of speeds. 120 is the *difference* in their individual distances, so it must be equated to the *difference* in their speeds. ### Final Answer Therefore, the correct answer is **1320 km**.