Train A running at a speed of 72 km/hr takes 24 seconds to completely cross train B running at 63 km/hr in the opposite direction. The length of train B is 1.5 times the length of train A. Train B crosses a bridge completely in 62 seconds. The length of the bridge (in m) is:​

Correct option is D

Given:

Speed of Train A = 72 km/h

Speed of Train B = 63 km/h

Train A crosses Train B (in opposite direction) in 24 seconds

Length of Train B = 1.5 × Length of Train A

Train B crosses a bridge in 62 seconds

Concept Used:

Speed conversion: 1 km/hr = 5/18 m/s

Relative speed (opposite direction) = sum of speeds

Distance = Speed × Time

Total length while crossing another object = combined lengths

Bridge length = Distance covered - length of train

Solution:

Speed of Train A = 72 × 5/18 = 20 m/s

Speed of Train B = 63 × 5/18 = 17.5 m/s

Relative speed = 20 + 17.5 = 37.5 m/s

Let length of Train A = x meters

Then, length of Train B = 1.5x meters

Total distance while crossing = x + 1.5x = 2.5x

2.5x = 37.5 × 24 => x = (37.5 × 24) / 2.5 = 360 m

Length of Train A = 360 m, Length of Train B = 1.5 × 360 = 540 m

Train B crosses a bridge in 62 seconds:

Distance = 17.5 × 62 = 1085 m

Length of bridge = 1085 - 540 = 545 m

Length of the bridge = 545.0 m