Shortcut Trick When two trains of equal length cross a pole in time t_(1) and t_(2), the time taken to cross each other in the same direction is given by: Time = (2 × t_(1) × t_(2)) ÷ (t_(2) − t_(1)) Given: t_(1) = 10 s, t_(2) = 20 s Required Time = (2 × 10 × 20) ÷ (20 − 10) = 400 ÷ 10 = 40 s ∴ The correct answer is 40 sec. Alternate Method Given: Length of each train = L (equal length) Time taken by Train 1 to cross the pole = 10 s Time taken by Train 2 to cross the pole = 20 s Calculations: ⇒ Speed of Train 1 (S_(1)) = Distance ÷ Time = L ÷ 10 ⇒ Speed of Train 2 (S_(2)) = Distance ÷ Time = L ÷ 20 ⇒ Relative Speed (Same direction) = S_(1) − S_(2) = L/10 − L/20 ⇒ Relative Speed = (2L − L) ÷ 20 = L/20 ⇒ Total Distance to cross each other = L + L = 2L ⇒ Time taken = Total Distance ÷ Relative Speed ⇒ Time = 2L ÷ (L/20) = 2L × (20 ÷ L) = 40 s ∴ The correct answer is 40 sec. Related Concepts: Relative Speed: Opposite Direction When two objects move in opposite directions, their speeds are added: S_(rel) = S_(1) + S_(2). Relative Speed: Same Direction When two objects move in the same direction, their speeds are subtracted: S_(rel) = S_(1) − S_(2). Crossing Objects of Equal Length Time taken to cross each other in opposite direction = (2 × t_(1) × t_(2)) ÷ (t_(1) + t_(2)). Crossing a Pole vs. Platform To cross a pole, distance = Length of train. To cross a platform, distance = Length of train + Length of platform.