A train travels 500m in first minute. In the next 4 minutes, it travels in each minute 125m more than that in the previous minute. The average speed per hour of the train during those 5 minutes will be

Options

A. 30 km/hr
B. 45km/hr
C. 50 km/hr
D. 55 km/hr

Answer

To solve the problem, we need to calculate the total distance traveled by the train in 5 minutes and then determine the average speed in kilometers per hour.

### Step-by-Step Solution:

1. **Distance in the First Minute**:
The train travels 500 meters in the first minute.
\[ \text{Distance in 1st minute} = 500 \text{ meters} \]

2. **Distance in the Next 4 Minutes**:
The train travels 125 meters more than the previous minute for the next 4 minutes.
- **2nd Minute**:
\[ 500 + 125 = 625 \text{ meters} \]
- **3rd Minute**:
\[ 625 + 125 = 750 \text{ meters} \]
- **4th Minute**:
\[ 750 + 125 = 875 \text{ meters} \]
- **5th Minute**:
\[ 875 + 125 = 1000 \text{ meters} \]

3. **Total Distance Traveled**:
Now, we add the distances traveled in all 5 minutes.
\[ \text{Total Distance} = 500 + 625 + 750 + 875 + 1000 \]
\[ \text{Total Distance} = 3750 \text{ meters} \]

4. **Convert Distance to Kilometers**:
To find the average speed in kilometers per hour, we first convert the total distance from meters to kilometers.
\[ \text{Total Distance in km} = \frac{3750}{1000} = 3.75 \text{ km} \]

5. **Convert Time to Hours**:
The total time is 5 minutes. We convert this to hours.
\[ \text{Time in hours} = \frac{5}{60} = \frac{1}{12} \text{ hours} \]

6. **Calculate Average Speed**:
Average speed is calculated using the formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]
\[ \text{Average Speed} = \frac{3.75 \text{ km}}{\frac{1}{12} \text{ hours}} = 3.75 \times 12 = 45 \text{ km/h} \]

### Final Answer:
The average speed of the train during those 5 minutes is **45 km/h**.

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