Question

A passenger sitting in a train A moving at 90 km/h observes another train B moving in the opposite direction for 8 s. If the velocity of train B is 54 km/h, then the length of train B is:

• A. 100 m
• B. 320 m
• C. 200 m
• D. 400 m

Answer 1

The Correct Option is B

To find the length of train B, we need to determine the relative velocity of the two trains as observed from train A, and then use this to calculate the length. Here's how to solve the problem step-by-step:

1. Identify the velocities:
   • Velocity of train A, \(V_A = 90 \text{ km/h}\).
   • Velocity of train B, \(V_B = 54 \text{ km/h}\).
2. Calculate the relative velocity:

Since both trains are moving in opposite directions, the relative velocity \(V_{R}\) is the sum of their speeds:

1. \(V_{R} = V_A + V_B = 90 + 54 = 144 \text{ km/h}.\)
2. Convert the relative velocity to m/s:

To convert from km/h to m/s, multiply by \(\frac{5}{18}\):

1. \(V_{R} = 144 \times \frac{5}{18} = 40 \text{ m/s}.\)
2. Use the formula: Distance = Speed × Time

The time duration for which train B is observed is 8 seconds. Therefore, the length of train B, which is the distance it covers in that time, is given by:

1. \(Length = V_{R} \times \text{Time} = 40 \times 8 = 320 \text{ meters}.\)

Therefore, the length of train B is 320 m. This makes option 320 m the correct answer.