Question

A train 180 m long crosses a platform 320 m long in 25 seconds. The speed of the train is:

• A. 60 km/h
• B. 72 km/h
• C. 80 km/h
• D. 90 km/h

Hint:

To easily handle speed conversions under exam conditions, remember the standard 5-to-18 ratio table: $$5 \text{ m/s} = 18 \text{ km/h}$$ $$10 \text{ m/s} = 36 \text{ km/h}$$ $$15 \text{ m/s} = 54 \text{ km/h}$$ $$\mathbf{20 \text{ m/s} = 72 \text{ km/h}}$$ Recognizing these common pairs saves precious calculation time!

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
When a train passes an object with a significant length of its own (such as a platform, bridge, or tunnel), the total distance covered by the train to completely clear that object is equal to the sum of the train's own length and the object's length. Since the measurements are given in meters and seconds, the initial speed will be calculated in meters per second ($\text{m/s}$), which then needs to be converted into kilometers per hour ($\text{km/h}$).

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

Step 3: Detailed Explanation:
From the given question: Length of the train $= 180 \text{ m}$ Length of the platform $= 320 \text{ m}$ Time taken $= 25 \text{ seconds}$ First, calculate the total distance traveled by the train: $$\text{Total Distance} = 180 + 320 = 500 \text{ meters}$$ Next, calculate the speed of the train in meters per second ($\text{m/s}$): $$\text{Speed} = \frac{500 \text{ m}}{25 \text{ s}} = 20 \text{ m/s}$$ Now, convert the speed into kilometers per hour ($\text{km/h}$) by multiplying with the standard factor $\frac{18}{5}$: $$\text{Speed} = 20 \times \frac{18}{5} \text{ km/h}$$ $$\text{Speed} = 4 \times 18 = 72 \text{ km/h}$$

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