Two trains start at the same time form A and B and proceed toward each other at the speed of 75 km/hr and 50 km/hr respectively. when both meet at a point in between, one train was found to have travelled 175 km more than the other. Find the distance between A and B.

### Concept & Logic When two objects travel for the same duration, the difference in distance covered is equal to the product of their speed difference and the time traveled. $$ \text{Distance Difference} = (\text{Speed}_1 - \text{Speed}_2) \times \text{Time} $$ ### Step-by-Step Solution 1. **Identify Given Values:** - Speed 1 = 75 km/hr. - Speed 2 = 50 km/hr. - Distance difference = 175 km. 2. **Calculate Speed Difference:** - $75 - 50 = 25$ km/hr. 3. **Find Travel Time:** - Time ($T$) = $\frac{175}{25} = 7$ hours. 4. **Calculate Total Distance:** - Relative speed = $75 + 50 = 125$ km/hr. - Total distance = $\text{Relative Speed} \times T = 125 \times 7 = 875$ km. ### Exam Strategy & Shortcut Instead of solving for individual distances, find the time they took to create the 175 km gap ($175 / 25 = 7$), then multiply that exact time by the sum of their speeds to get the total distance instantly. ### Common Pitfall Multiplying the time by the individual speeds instead of the relative speed when attempting to find the total distance between the two stations. ### Final Answer Therefore, the correct answer is **875 km**.