A train travels 500 m in first minute. In the next 4 minute. It travels in each minute 125 m 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. 45 km / hr
C. 50 km/hr
D. 55 km /hr

Answer

To find the average speed of the train over the 5 minutes, we will calculate the total distance traveled during that time and then use the formula for average speed.

### Step-by-Step Solution:

1. **Distance in the First Minute**:
- The train travels 500 meters in the first minute.

2. **Distance in the Next Four Minutes**:
- In the second minute, the train travels \(500 + 125 = 625\) meters.
- In the third minute, the train travels \(625 + 125 = 750\) meters.
- In the fourth minute, the train travels \(750 + 125 = 875\) meters.
- In the fifth minute, the train travels \(875 + 125 = 1000\) meters.

3. **Total Distance Traveled**:
- Now, we will sum up the distances traveled in each of the 5 minutes:
\[ \text{Total Distance} = 500 + 625 + 750 + 875 + 1000 \]
- Calculating this:
\[ 500 + 625 = 1125 \\ 1125 + 750 = 1875 \\ 1875 + 875 = 2750 \\ 2750 + 1000 = 3750 \text{ meters} \]

4. **Convert Distance to Kilometers**:
- Since 1 kilometer = 1000 meters, we convert the total distance:
\[ \text{Distance in kilometers} = \frac{3750}{1000} = 3.75 \text{ kilometers} \]

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

6. **Calculate Average Speed**:
- The formula for average speed is:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]
- Substituting the values we have:
\[ \text{Average Speed} = \frac{3.75 \text{ km}}{\frac{1}{12} \text{ hours}} = 3.75 \times 12 = 45 \text{ km/h} \]

### Final Answer:
The average speed of the train during those 5 minutes is **45 kilometers per hour**.