Question

A train travelling at 72 km/h crosses a platform of length 180 m in 24 seconds. What is the length of the train?

• A. 240 m
• B. 300 m
• C. 360 m
• D. 480 m

Hint:

Always convert units first.
A common shortcut to remember is that $18 \text{ km/h} = 5 \text{ m/s}$.
Since $72 \text{ km/h}$ is $4 \times 18 \text{ km/h}$, the speed is directly $4 \times 5 = 20 \text{ m/s}$.
Multiplying this by $24 \text{ seconds}$ gives $480 \text{ m}$ of total distance.
Subtract the platform's length of $180 \text{ m}$ to get the train length of $300 \text{ m}$ instantly.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
This problem belongs to the topic of Time, Speed, and Distance, specifically focusing on train-related problems.
When a train crosses a platform, the total distance covered by the train is equal to the sum of the length of the train itself and the length of the platform.
We are given the speed of the train in km/h, the length of the platform in meters, and the time taken to cross the platform in seconds.
Our objective is to determine the length of the train.

Step 2: Key Formula or Approach:
1. Conversion of speed from km/h to m/s:
\[ \text{Speed in m/s} = \text{Speed in km/h} \times \frac{5}{18} \]
2. Distance formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
3. Total distance when crossing a platform:
\[ \text{Total Distance} = \text{Length of Train } (L) + \text{Length of Platform } (P) \]

Step 3: Detailed Explanation:
$\bullet$ First, we need to convert the speed of the train from km/h to m/s to match the unit of length (meters) and time (seconds).
$\bullet$ Given Speed $= 72 \text{ km/h}$.
\[ \text{Speed in m/s} = 72 \times \frac{5}{18} = 4 \times 5 = 20 \text{ m/s} \]
$\bullet$ Let the length of the train be $L$ meters.
$\bullet$ The length of the platform is given as $180 \text{ m}$.
$\bullet$ The total distance covered by the train while completely crossing the platform is:
\[ \text{Distance} = L + 180 \]
$\bullet$ The time taken to cover this distance is given as $24 \text{ seconds}$.
$\bullet$ Applying the distance-speed-time relationship:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
\[ L + 180 = 20 \times 24 \]
\[ L + 180 = 480 \]
$\bullet$ Solving for the length of the train $L$:
\[ L = 480 - 180 \]
\[ L = 300 \text{ meters} \]

Step 4: Final Answer:
The length of the train is 300 meters.
Therefore, the correct option is (B).