A train T₁ traveling at 93 km/hr crosses another train T₂ whose length is half of the length of first train, moving in opposite direction at 51 km/hr, in 24 seconds. If the train T₁ passes a bridge in 1 minute and 6 seconds, then the length of that bridge (in meters) is

Correct option is C

Given information:

• Train T₁ speed: 93 km/hr
• Train T₂ speed: 51 km/hr (opposite direction)
• Length of T₂ = (1/2) × Length of T₁
• Time for trains to cross each other: 24 seconds
• Time for T₁ to cross the bridge: 1 minute 6 seconds = 66 seconds

Step 1: Find the length of train T₁

Let the length of T₁ = L metersThen the length of T₂ = L/2 meters

When two trains cross each other moving in opposite directions, their relative speed is the sum of their speeds.

Relative speed = 93 + 51 = 144 km/hr

Converting to m/s: 144 × (5/18) = 40 m/s

When the trains cross each other, the total distance covered equals the sum of their lengths:

• Distance = L + L/2 = 3L/2 meters
• Time = 24 seconds
• Speed = 40 m/s

Using Distance = Speed × Time:3L/2 = 40 × 243L/2 = 9603L = 1920L = 640 meters

So, train T₁ has length 640 meters.

Step 2: Find the length of the bridge

When train T₁ crosses the bridge, it travels a distance equal to its own length plus the bridge length.

Speed of T₁ = 93 km/hr = 93 × (5/18) = 25.83̄ m/s (or 775/30 m/s)

Let the bridge length = B meters

Distance covered = Length of train + Length of bridge = 640 + BTime = 66 seconds

Using Distance = Speed × Time:640 + B = 25.83̄ × 66640 + B = 93 × (5/18) × 66640 + B = 93 × 5 × 66/18640 + B = 93 × 5 × 11/3640 + B = 465 × 11/3640 + B = 5115/3640 + B = 1705

B = 1705 - 640 = 1065 meters

The length of the bridge is 1065 meters.