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: Calculate the total time taken

The journey starts on 4th June 2020 at 22:30 hours and ends on 6th June 2020 at 04:30 hours.

Let's break down the duration into distinct intervals:

1. Time spent on 4th June 2020:
From 22:30 hours to 24:00 (midnight) = 1 hour 30 minutes = 1.5 hours.

2. Time spent on 5th June 2020:
The train runs for the full day (24 hours).

3. Time spent on 6th June 2020:
From 00:00 (midnight) to 04:30 hours = 4 hours 30 minutes = 4.5 hours.

Now, add these time intervals together to get the total time taken:

$\text{Total Time}=1.5\text{hours}+24\text{hours}+4.5\text{hours}$

$\text{Total Time}=30\text{hours}$

Step 2: Note the total distance

$\text{Total Distance}=1145\text{km}$

Step 3: Calculate the average speed

The formula for average speed is:

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

Substituting the values into the formula:

$\text{Average Speed}=\frac{1145}{30}$

$\text{Average Speed}=38.166\text{... km/h}$

Rounding off to the nearest value, the average speed of the train was nearly 38.5 km/h (matching the given option).