A train without stoppage travels with an average speed of 80 km/h and with stoppage. It travels with an average speed of 64 km/h. For how many minutes does the train stop on an average per hour ?

Options

A. 12
B. 8
C. 10
D. 14

Answer

To solve the problem, we need to determine how many minutes the train stops on average per hour. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Speeds
- The train travels without stoppage at an average speed of **80 km/h**.
- The train travels with stoppage at an average speed of **64 km/h**.

### Step 2: Calculate the Difference in Speed
- The difference in speed when the train is not stopping and when it is stopping is:
\[ \text{Difference in speed} = 80 \text{ km/h} - 64 \text{ km/h} = 16 \text{ km/h} \]

### Step 3: Relate Speed to Distance and Time
- We know that speed is defined as:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
- If we consider the time taken to travel for **1 hour** (which is 60 minutes), the distance the train would have covered without stoppage is:
\[ \text{Distance without stoppage} = 80 \text{ km} \]
- The distance covered with stoppage is:
\[ \text{Distance with stoppage} = 64 \text{ km} \]

### Step 4: Calculate the Distance Lost Due to Stoppage
- The distance that the train could not cover due to stoppage in that hour is:
\[ \text{Distance lost} = 80 \text{ km} - 64 \text{ km} = 16 \text{ km} \]

### Step 5: Calculate the Time Taken for the Lost Distance
- The time taken to cover the lost distance (16 km) at the speed of 80 km/h is calculated as follows:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{16 \text{ km}}{80 \text{ km/h}} = 0.2 \text{ hours} \]

### Step 6: Convert Time from Hours to Minutes
- To convert the time from hours to minutes, we multiply by 60:
\[ \text{Time in minutes} = 0.2 \text{ hours} \times 60 \text{ minutes/hour} = 12 \text{ minutes} \]

### Conclusion
- Therefore, the train stops on average for **12 minutes** per hour.