Two trains, each 100 m long, moving in opposite directions, cross each other in 8 seconds. If one is moving twice as fast the other, then the speed of the faster train is :

### Concept & Relative Speed When two trains move in opposite directions, their relative speed is the sum of their individual speeds. They must cover a distance equal to the sum of their lengths to cross each other. $$ \text{Relative Speed} = \frac{\text{Total Length}}{\text{Time}} $$ ### Step-by-Step Solution * Total distance to cover = Sum of lengths = $100 + 100 = 200$ meters. * Time taken to cross = 8 seconds. * Relative speed in m/s = $\frac{200}{8} = 25$ m/s. * Convert relative speed to km/hr: $25 \times \frac{18}{5} = 90$ km/hr. * Let the speed of the slower train be $x$ km/hr. The faster train is $2x$ km/hr. * Relative speed = $x + 2x = 3x$. * Equating speeds: $3x = 90 \Rightarrow x = 30$ km/hr. * Speed of the faster train = $2x = 60$ km/hr. ### Exam Strategy & Shortcut Calculate relative speed directly in m/s, assign ratios (1:2 means 3 parts total), find the value of one part ($25 / 3$ m/s), and then calculate the faster train's speed before converting: $2 \times \frac{25}{3} \times \frac{18}{5} = 60$ km/hr. ### Common Pitfall Forgetting to convert the relative speed from m/s to km/hr before finding the individual speeds, leading to incorrect choices. ### Final Answer Therefore, the correct answer is **60 km/hr**.