A boy boarded a train on 4th June, 2020 at Nagarcoil for Madgaon. The train departed at 22:30 hours from Nagarcoil and reached Madgaon at 04:30 hours on 6th June, 2020. If the distance covered by the train during this time interval is 1145 km, the average speed of the train was nearly

The correct option is 38.5 km/h.

To find the average speed of the train, we need to calculate the total distance traveled and the total time taken for the journey.

Step 1: Determine the total distance covered
Given distance = 1145 km

Step 2: Calculate the total time taken
- On 4th June 2020: The train departed at 22:30 hours.
Time traveled on 4th June = 24:00 - 22:30 = 1 hour 30 minutes (1.5 hours)

- On 5th June 2020: The train traveled for the entire day.
Time traveled on 5th June = 24 hours

- On 6th June 2020: The train reached Madgaon at 04:30 hours.
Time traveled on 6th June = 4 hours 30 minutes (4.5 hours)

Total time taken = 1.5 hours + 24 hours + 4.5 hours = 30 hours

Step 3: Calculate the average speed
The formula for average speed is:

$\text{Average Speed}=\frac{\text{Total Distance}}{\text{Total Time}}$

Substituting the given values into the formula:

$\text{Average Speed}=\frac{1145\text{km}}{30\text{hours}}\approx 38.16\text{km/h}$

Rounding off to the nearest available option, the average speed of the train was nearly 38.5 km/h.