
Shortcut Trick
Relative speed in opposite direction = 93 + 51 = 144 kmph = 144 × (5/18) = 40 m/s.
Total distance (Length A + Length B) = 40 × 18 = 720 m.
Since B = A/2, then A + A/2 = 720 ⇒ 1.5A = 720 ⇒ A = 480 m.
Distance covered by A in 42s = (93 × 5/18) × 42 = 1085 m.
Length of bridge = 1085 − 480 = 605 m.
∴ The correct answer is 605 m.

Alternate Method
Given: Speed of Train A = 93 km/hr, Speed of Train B = 51 km/hr, Crossing time = 18 s, Bridge crossing time = 42 s.
Formula Used: Relative Speed = S1 + S2 (Opposite); Distance = Speed × Time; 1 km/hr = 5/18 m/s.

⇒ Relative Speed = (93 + 51) × (5/18) = 144 × (5/18) = 40 m/s.
⇒ Let Length of Train A = 2x and Train B = x.
⇒ Total Length = 2x + x = 40 × 18 ⇒ 3x = 720 ⇒ x = 240 m.
⇒ Length of Train A = 2 × 240 = 480 m.
⇒ Speed of Train A in m/s = 93 × (5/18) = 15.5 × (5/3) = 25.833... or 310/12 = 155/6 m/s.
⇒ Total Distance for bridge crossing = Length A + Bridge = (155/6) × 42.
⇒ 480 + Bridge = 155 × 7 = 1085 m.
⇒ Bridge = 1085 − 480 = 605 m.
∴ The correct answer is 605 m.

Additional Information
Relative Speed Concept
When two objects move in the opposite direction, relative speed is S1 + S2. When they move in the same direction, it is |S1 − S2|.
Crossing a Bridge/Platform
When a train crosses a stationary object of length L, the total distance covered is the sum of the length of the train and the length of the object.
Unit Conversion
To convert km/hr to m/s, multiply by 5/18. To convert m/s to km/hr, multiply by 18/5.