A person boarded an express train on 29th November, 2019 at Surat (Gujarat) for Nagarcoil (Kerala). The train departed from Surat at 19:45 hours and reached Nagarcoil at 11:45 hours on 1st December, 2019. If the distance between Surat and Nagarcoil by train route is nearly 2120 km, the average speed of the train during this journey was

The correct option is 53 km/h.

To find the average speed of the train during the journey, we need to determine two main quantities:
1. Total distance traveled by the train
2. Total time taken for the journey

Step 1: Given Information
Departure time from Surat: 29th November, 2019 at 19:45 hours
Arrival time at Nagarcoil: 1st December, 2019 at 11:45 hours
Total distance between Surat and Nagarcoil = 2120 km

Step 2: Calculate Total Time Taken
Let us break down the time taken across each day of travel:

• 29th November 2019:
The train starts at 19:45 hours. Since a day has 24 hours (or 24:00 hours):
Time traveled on 29th November = 24:00 - 19:45 = 4 hours 15 minutes

• 30th November 2019:
November has 30 days, so the train travels for the entire day of 30th November.
Time traveled on 30th November = 24 hours

• 1st December 2019:
The train reaches Nagarcoil at 11:45 hours.
Time traveled on 1st December = 11 hours 45 minutes

• Total Journey Time:
Total time = (4 hours 15 minutes) + (24 hours) + (11 hours 45 minutes)
Adding the minutes together: 15 minutes + 45 minutes = 60 minutes = 1 hour.
Adding all the hours: 4 + 24 + 11 + 1 = 40 hours.

Step 3: Calculate Average Speed
The formula for average speed is:

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

Substituting the values into the formula:

$\text{Average Speed}=\frac{2120\text{km}}{40\text{hours}}$

$\text{Average Speed}=53\text{km/h}$

Thus, the average speed of the train during this journey was 53 km/h.