Question

A train 240 m long crosses a platform 360 m long in 30 seconds. The speed of the train is:

• A. 48 km/h
• B. 60 km/h
• C. 72 km/h
• D. 84 km/h

Hint:

Remember the inverse unit-conversion multiplier rules to save time! $\text{km/h} \longrightarrow \text{m/s}$ : Multiply by $\frac{5}{18}$ $\text{m/s} \longrightarrow \text{km/h}$ : Multiply by $\frac{18}{5}$ Since $20 \text{ m/s}$ is a standard multiple of 5 ($5 \times 4$), its corresponding $\text{km/h}$ value will be the same multiple of 18 ($18 \times 4 = 72$).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
When a train passes an object that has its own significant physical length (like a platform, bridge, or another train), the total distance traveled by the train while completely clearing that object is equal to the sum of the train's length and the object's length. Since the measurements are provided in meters and seconds, the initial calculated speed will be in meters per second (m/s). We must convert this value into kilometers per hour (km/h) to match the options.

Step 2: Key Formula or Approach:
1. $\text{Total Distance} = \text{Length of Train} + \text{Length of Platform}$ 2. $\text{Speed (in m/s)} = \frac{\text{Total Distance}}{\text{Total Time Taken}}$ 3. To convert speed from $\text{m/s}$ to $\text{km/h}$, multiply the value by $\frac{18}{5}$.

Step 3: Detailed Explanation:
Given values from the problem statement: $\text{Length of the train} = 240 \text{ m}$ $\text{Length of the platform} = 360 \text{ m}$ $\text{Time taken to cross} = 30 \text{ seconds}$ First, calculate the total distance covered by the train: \[ \text{Total Distance} = 240 + 360 = 600 \text{ meters} \] Now, calculate the speed of the train in meters per second (m/s): \[ \text{Speed} = \frac{600 \text{ m}}{30 \text{ s}} = 20 \text{ m/s} \] Convert this speed into kilometers per hour (km/h) by scaling it with the standard factor of $\frac{18}{5}$: \[ \text{Speed} = 20 \times \frac{18}{5} \text{ km/h} \] Dividing 20 by 5 gives 4: \[ \text{Speed} = 4 \times 18 = 72 \text{ km/h} \]

Step 4: Final Answer:
The speed of the train is 72 km/h.