A train moves with a speed of 30 kmph for 12 minutes and for next 8 minutes at a speed of 45 kmph. Find the average speed of the train.

Options

A. 37.5kmph
B. 36 kmph
C. 48 kmph
D. 30 kmph

Answer

To find the average speed of the train, we will follow these steps:

### Step 1: Calculate the distance covered in the first part of the journey
- Speed = 30 km/h
- Time = 12 minutes

First, we need to convert the time from minutes to hours:
\[ \text{Time in hours} = \frac{12 \text{ minutes}}{60} = \frac{1}{5} \text{ hours} \]

Now, we can calculate the distance:
\[ \text{Distance} = \text{Speed} \times \text{Time} = 30 \text{ km/h} \times \frac{1}{5} \text{ h} = 6 \text{ km} \]

### Step 2: Calculate the distance covered in the second part of the journey
- Speed = 45 km/h
- Time = 8 minutes

Again, convert the time from minutes to hours:
\[ \text{Time in hours} = \frac{8 \text{ minutes}}{60} = \frac{2}{15} \text{ hours} \]

Now, we can calculate the distance:
\[ \text{Distance} = \text{Speed} \times \text{Time} = 45 \text{ km/h} \times \frac{2}{15} \text{ h} = 6 \text{ km} \]

### Step 3: Calculate the total distance
Now, we can find the total distance covered by the train:
\[ \text{Total Distance} = 6 \text{ km} + 6 \text{ km} = 12 \text{ km} \]

### Step 4: Calculate the total time taken
Now, we need to find the total time taken for the journey:
\[ \text{Total Time} = 12 \text{ minutes} + 8 \text{ minutes} = 20 \text{ minutes} \]

Convert the total time into hours:
\[ \text{Total Time in hours} = \frac{20 \text{ minutes}}{60} = \frac{1}{3} \text{ hours} \]

### Step 5: Calculate the average speed
Finally, we can calculate the average speed using the formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{12 \text{ km}}{\frac{1}{3} \text{ h}} = 12 \times 3 = 36 \text{ km/h} \]

### Conclusion
The average speed of the train is **36 km/h**.

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