Question

A train running at 72 km/h crosses a pole in 20 seconds. The length of the train is:

• A. 320 m
• B. 360 m
• C. 400 m
• D. 420 m

Hint:

Keep the basic multi-units of 18 memorized for quick conversions: $18\text{ km/h} = 5\text{ m/s}$, $36\text{ km/h} = 10\text{ m/s}$, $54\text{ km/h} = 15\text{ m/s}$, and $72\text{ km/h} = 20\text{ m/s}$. Recognizing these multiples saves valuable calculation time!

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
When a train crosses a stationary pole or a point object of negligible width, the total distance traveled by the train while passing it is exactly equal to its own length. Because the time is given in seconds and the answer choices are in meters, we must first convert the train's speed from kilometers per hour (km/h) to meters per second (m/s).

Step 2: Key Formula or Approach:
1. To convert speed from $\text{km/h}$ to $\text{m/s}$, multiply by $\frac{5}{18}$. 2. $\text{Distance} = \text{Speed} \times \text{Time}$ 3. $\text{Length of the train} = \text{Distance traveled}$

Step 3: Detailed Explanation:
Given parameters: $\text{Speed of the train} = 72 \text{ km/h}$ $\text{Time taken} = 20 \text{ seconds}$ Convert the speed into $\text{m/s}$: \[ \text{Speed} = 72 \times \frac{5}{18} \text{ m/s} \] Dividing 72 by 18 gives 4: \[ \text{Speed} = 4 \times 5 = 20 \text{ m/s} \] Now, calculate the length of the train using the distance formula: \[ \text{Length of train} = \text{Speed (in m/s)} \times \text{Time (in seconds)} \] \[ \text{Length of train} = 20 \text{ m/s} \times 20 \text{ s} = 400 \text{ meters} \]

Step 4: Final Answer:
The length of the train is 400 m.