A person boarded an express train on 3oth August 2015 at Ahmedabad for Trivandrum. The train departed from Ahmadabad at 13:30 hand reached Trivandrum at 7: 30 hon let September 2015. If the distance between Ahmadabad and Trivandrum is 2268 km then, the average speed of the train between these two stations is

Options

A. 54 m/s
B. 42m/s
C. 15 m/s
D. 9 m/s

Answer

To find the average speed of the train between Ahmedabad and Trivandrum, we need to follow these steps:

### Step 1: Determine the total distance
The distance between Ahmedabad and Trivandrum is given as 2268 km.

### Step 2: Calculate the total travel time
1. **Departure Time**: The train departed from Ahmedabad at 13:30 on 30th August 2015.
2. **Arrival Time**: The train arrived in Trivandrum at 7:30 on 1st September 2015.

Now, we need to calculate the total time taken for the journey.

- From 30th August 2015, 13:30 to 31st August 2015, 13:30 is 24 hours.
- From 31st August 2015, 13:30 to 1st September 2015, 7:30 is:
- From 13:30 to 24:00 (midnight) = 10.5 hours
- From midnight to 7:30 = 7.5 hours
- Total for this part = 10.5 + 7.5 = 18 hours.

Now, adding these two time intervals together:
- Total time = 24 hours + 18 hours = 42 hours.

### Step 3: Calculate the average speed
The average speed can be calculated using the formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]

Substituting the values:
\[ \text{Average Speed} = \frac{2268 \text{ km}}{42 \text{ hours}} \]

Calculating this gives:
\[ \text{Average Speed} = 54 \text{ km/h} \]

### Step 4: Convert km/h to m/s (if needed)
To convert km/h to m/s, we use the conversion factor:
\[ 1 \text{ km/h} = \frac{5}{18} \text{ m/s} \]

So,
\[ 54 \text{ km/h} = 54 \times \frac{5}{18} = 15 \text{ m/s} \]

### Final Answer
The average speed of the train between Ahmedabad and Trivandrum is **54 km/h** or **15 m/s**.

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