Excluding stoppages, the speed of a train is 108 km/h and including stoppages, it is 90 km/h. For how many minutes does the train stop per hour?

Options

A. 5
B. 9
C. 10
D. 6

Answer

To solve the problem of how many minutes a train stops per hour, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the speeds**:
- Speed excluding stoppages = 108 km/h
- Speed including stoppages = 90 km/h

2. **Calculate the distance covered in one hour**:
- When the train runs without stoppages, it covers 108 km in 1 hour.
- When the train runs with stoppages, it covers 90 km in 1 hour.

3. **Determine the time taken to cover 90 km at the speed of 108 km/h**:
- We can find the time taken to cover 90 km at the speed of 108 km/h using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{90 \text{ km}}{108 \text{ km/h}} \]
- Simplifying this gives:
\[ \text{Time} = \frac{90}{108} \text{ hours} \]

4. **Convert the time from hours to minutes**:
- Since 1 hour = 60 minutes, we convert the time:
\[ \text{Time in minutes} = \frac{90}{108} \times 60 \]

5. **Calculate the value**:
- Simplifying the fraction:
\[ \frac{90}{108} = \frac{5}{6} \]
- Therefore:
\[ \text{Time in minutes} = \frac{5}{6} \times 60 = 50 \text{ minutes} \]

6. **Determine the stoppage time**:
- Since the train runs for 60 minutes in total and takes 50 minutes to cover the distance, the stoppage time is:
\[ \text{Stoppage time} = 60 \text{ minutes} - 50 \text{ minutes} = 10 \text{ minutes} \]

### Final Answer:
The train stops for **10 minutes** per hour.

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