A 180-metre long train crosses another 270-metre long train running in the opposite direction in 10.8 seconds. If the speed of the first train is 60 kmph, what is the speed of the second train in kmph? (Bank P.O., 2010)

### Concept & Converting Combined Distance To find an unknown speed in an opposite-direction crossing, first determine the total combined speed in m/s, convert it to km/hr, and then subtract the known speed. $$Relative\ Speed = \frac{L_1 + L_2}{Time}$$ ### Step-by-Step Solution 1. **Given:** $L_1 = 180$ m, $L_2 = 270$ m. Total distance = $180 + 270 = 450$ m. Time = 10.8 s. $S_1 = 60$ kmph. Let $S_2$ be the speed of the second train in kmph. 2. Calculate the relative speed in m/s: $$Relative\ Speed = \frac{450}{10.8} = \frac{4500}{108}\ m/s$$ 3. Convert this relative speed to km/hr: $$\frac{4500}{108} \times \frac{18}{5} = \frac{900}{108} \times 18 = \frac{900}{6} = 150\ km/hr$$ 4. Since they move in opposite directions, the relative speed is the sum of their individual speeds: $$S_1 + S_2 = 150$$ $$60 + S_2 = 150$$ 5. Solve for $S_2$: $$S_2 = 150 - 60 = 90\ km/hr$$ ### Exam Strategy & Shortcut Distance = 450m. Time = 10.8s. Speed in km/hr = $(450/10.8) \times (18/5) = 150$ km/hr. Since opposite direction means speeds are added, the second train's speed is $150 - 60 = 90$ km/hr. ### Common Pitfall Struggling with the decimal division ($450/10.8$). Always clear decimals by multiplying numerator and denominator by 10 before simplifying, and apply the $18/5$ conversion early to cancel out awkward denominators like 108 (since $18 \times 6 = 108$). ### Final Answer Therefore, the correct answer is **90**.