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: Change the speed into metres per second.
Speed is $72$ km/h. To get m/s, multiply by $\frac{5}{18}$, giving $72 \times \frac{5}{18} = 20$ m/s.

Step 2: Recall what the train must cover.
While crossing a platform, the train covers its own length plus the platform length.

Step 3: Find the total distance covered.
Distance is speed times time, so $20 \times 24 = 480$ m.

Step 4: Write the distance as a sum.
This $480$ m equals the train length plus the platform of $180$ m. \[ \text{train} + 180 = 480 \]

Step 5: Subtract the platform length.
Train length $= 480 - 180 = 300$ m.

Step 6: State the answer.
The train is $300$ m long. \[ \boxed{300 \text{ m}} \]