Question

A train running at the speed of 80 km/h crosses a 450 m long tunnel in 36 seconds. The length of the train (in m) is:

• A. 350
• B. 380
• C. 420
• D. 450

Hint:

Always ensure unit consistency. Since the options and tunnel length are in meters and the time is in seconds, converting the speed from \(\text{km/h}\) to \(\text{m/s}\) at the beginning is a necessary step.
Multiplying by \(\frac{5}{18}\) is the standard shortcut to convert from \(\text{km/h}\) to \(\text{m/s}\).

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
A moving train crosses a tunnel of a given length. We are given the speed of the train, the length of the tunnel, and the time taken to cross the tunnel. We need to find the length of the train.

Step 2: Key Formula or Approach:
The fundamental relation is:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
When a train crosses a tunnel, the total distance covered is the sum of the length of the train and the length of the tunnel:
\[ \text{Total Distance} = L_{\text{train}} + L_{\text{tunnel}} \]
We must convert the speed from \(\text{km/h}\) to \(\text{m/s}\) using the conversion factor:
\[ 1\text{ km/h} = \frac{5}{18}\text{ m/s} \]

Step 3: Detailed Explanation:
1. Let the length of the train be \( L \) meters.
2. The length of the tunnel is given as \( 450\text{ m} \).
3. The total distance to be covered by the train to completely clear the tunnel is:
\[ \text{Distance} = L + 450 \]
4. The speed of the train is given as \( 80\text{ km/h} \). We convert this into meters per second (\(\text{m/s}\)):
\[ \text{Speed} = 80 \times \frac{5}{18} = \frac{400}{18} = \frac{200}{9}\text{ m/s} \]
5. The time taken to cross the tunnel is given as \( 36\text{ seconds} \).
6. Now, using the formula \( \text{Distance} = \text{Speed} \times \text{Time} \):
\[ L + 450 = \frac{200}{9} \times 36 \]
7. Simplifying the expression on the right-hand side:
\[ L + 450 = 200 \times 4 \]
\[ L + 450 = 800 \]
8. Solving for \( L \):
\[ L = 800 - 450 = 350\text{ m} \]
9. Thus, the length of the train is 350 meters.

Step 4: Final Answer:
The length of the train is 350 meters, which corresponds to option (A).