Question

A 150 m long train is going at a speed of 72 km/hr. It will cross a 130 m long railway bridge in :

• A. 14 sec
• B. 18.8 sec
• C. 21.4 sec
• D. 35.6 sec

Hint:

Always remember that a speed of $18 \text{ km/hr}$ is exactly equal to $5 \text{ m/s}$.
Since $72 \text{ km/hr}$ is $4 \times 18$, the speed in $\text{m/s}$ must be $4 \times 5 = 20 \text{ m/s}$.
Remembering multiples of $18$ helps perform unit conversions instantly.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks for the time taken by a train of a given length to cross a bridge of a known length at a specified speed.
To completely cross the bridge, the rear end of the train must pass the far end of the bridge.
Thus, the total distance covered during this event is the sum of the train's length and the bridge's length.

Step 2: Key Formula or Approach:
The relation between distance, speed, and time is:
\[ \text{Time } (t) = \frac{\text{Total Distance } (D)}{\text{Speed } (v)} \] The total distance is:
\[ D = \text{Length of train } (L_{\text{train}}) + \text{Length of bridge } (L_{\text{bridge}}) \] The speed must be converted from $\text{km/hr}$ to $\text{m/s}$ to keep the units consistent.

Step 3: Detailed Explanation:

• Calculate Total Distance ($D$):
Given:
Length of train $= 150 \text{ m}$
Length of bridge $= 130 \text{ m}$
\[ D = 150 + 130 = 280 \text{ meters} \]

• Convert Speed to m/s:
The speed of the train is $72 \text{ km/hr}$.
To convert to $\text{m/s}$, multiply by $\frac{5}{18}$:
\[ v = 72 \times \frac{5}{18} = 4 \times 5 = 20 \text{ m/s} \]

• Calculate the Time Taken ($t$):
Use the time formula:
\[ t = \frac{D}{v} = \frac{280}{20} = 14 \text{ seconds} \]

Step 4: Final Answer:
The train will cross the bridge in $14 \text{ seconds}$.
Therefore, the correct option is (A).