A train 800 metres long is running at the speed of 78 kmhr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in metres) is

Options

A. 77200
B. 500
C. 1300
D. 13

Answer

To find the length of the tunnel that the train crosses, we can use the formula for time, which is:

\[ \text{Time} = \frac{\text{Length of Train} + \text{Length of Tunnel}}{\text{Speed of Train}} \]

### Step-by-step Solution:

1. **Convert the time from minutes to seconds:**
- Given time = 1 minute = 60 seconds.

2. **Identify the length of the train:**
- Length of the train = 800 meters.

3. **Convert the speed from km/hr to m/s:**
- Given speed = 78 km/hr.
- To convert km/hr to m/s, use the conversion factor \( \frac{5}{18} \):
\[ \text{Speed in m/s} = 78 \times \frac{5}{18} = \frac{390}{18} = 21.67 \text{ m/s} \text{ (approximately)} \]

4. **Set up the equation using the time formula:**
\[ 60 = \frac{800 + x}{21.67} \]
where \( x \) is the length of the tunnel.

5. **Multiply both sides by the speed to eliminate the fraction:**
\[ 60 \times 21.67 = 800 + x \]
\[ 1300.2 = 800 + x \]

6. **Solve for \( x \):**
\[ x = 1300.2 - 800 \]
\[ x = 500.2 \text{ meters (approximately 500 meters)} \]

7. **Conclusion:**
- The length of the tunnel is approximately 500 meters.

### Final Answer:
The length of the tunnel is **500 meters**.