Train A running at a speed of 63 km/h takes 21 seconds to completely cross train B running at 45 km/h the opposite direction. The length of train B is 2.5 times the length of train A. Train B crosses a bridge completely in 76 seconds. The length of the bridge (in m) is:

Correct option is D

Given:

Speed of Train A = 63 km/h

Speed of Train B = 45 km/h

Time taken by Train A to cross Train B = 21 seconds

Length of Train B = 2.5 times the length of Train A

Time taken by Train B to cross a bridge = 76 seconds

Formula Used:

Distance = Speed × Time

Solution:

Let the length of Train A be L. Then, the length of Train B is 2.5L.

Relative speed of Train A and Train B:

Relative Speed = 63 + 45 = 108 km/h

Convert the relative speed to meters per second:

Relative Speed =$$\frac{108 \times 1000}{3600}$$​ = 30 m/s

Distance = Length of Train A + Length of Train B = L + 2.5L = 3.5L

Using the formula:

3.5L = 30 × 21 = 630

L = $$\frac{630}{3.5}$$​ = 180 meters

So, the length of Train A is 180 meters. The length of Train B is:

2.5L = 2.5 × 180 = 450 meters
Let the length of the bridge be B.

So,

First, convert the speed of Train B into meters per second:

Speed of Train B = $$\frac{45 \times 1000}{3600}$$​ = 12.5 m/s

The total distance covered is:

450 + B = 12.5 × 76 = 950

So, the length of the bridge is:

B = 950 – 450 = 500 meters