Shortcut Trick
Relative Speed in opposite direction = 58 + 50 = 108 km/h = 108 × 5/18 = 30 m/s.
Total distance (LX + LY) = Speed × Time = 30 × 16 = 480 m.
Since LY = 3 × LX, total 4 units = 480 m ⇒ 1 unit (LX) = 120 m and 3 units (LY) = 360 m.
Speed of Y = 50 × 5/18 = 125/9 m/s. Bridge Crossing: (360 + B) = (125/9) × 54 = 125 × 6 = 750 m.
Length of Bridge (B) = 750 − 360 = 390 m.
∴ The correct answer is 390 m.
Alternate Method
Given: Speed of X = 58 km/h, Speed of Y = 50 km/h, Time to cross = 16 s, LY = 3LX, Time for bridge = 54 s.
Formula: Distance = Relative Speed × Time; Speed (m/s) = Speed (km/h) × 5/18.
⇒ Relative Speed = (58 + 50) × 5/18 = 108 × 5/18 = 30 m/s
⇒ LX + LY = 30 × 16 = 480 m
⇒ LX + 3LX = 480 ⇒ 4LX = 480 ⇒ LX = 120 m
⇒ LY = 3 × 120 = 360 m
⇒ Speed of Train Y = 50 × 5/18 = 125/9 m/s
⇒ Distance covered in 54 s = (125/9) × 54 = 125 × 6 = 750 m
⇒ Bridge length + LY = 750 ⇒ Bridge length + 360 = 750
⇒ Bridge length = 750 − 360 = 390 m
∴ The correct answer is 390 m.
Additional Information
Relative Speed Concept
When two objects move in the opposite direction, relative speed is the sum of their speeds (S1 + S2). In the same direction, it is the difference (S1 − S2).
Train Crossing Distance
When a train crosses another train or a bridge, the total distance covered is equal to the sum of the lengths of the train and the object being crossed.
Speed Unit Conversion
To convert km/h to m/s, multiply by 5/18. To convert m/s to km/h, multiply by 18/5.