Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour ?

Options

A. 9
B. 10
C. 12
D. 20

Explanation

To find out how many minutes the bus stops per hour, we can follow these steps:

### Step 1: Understand the given speeds
- Speed of the bus excluding stoppages = 54 km/h
- Speed of the bus including stoppages = 45 km/h

### Step 2: Calculate the difference in speed
The difference in speed due to stoppages can be calculated as follows:
\[ \text{Difference in speed} = \text{Speed excluding stoppages} - \text{Speed including stoppages} \]
\[ \text{Difference in speed} = 54 \text{ km/h} - 45 \text{ km/h} = 9 \text{ km/h} \]

### Step 3: Use the formula to find stoppage time
We can use the formula for calculating the time the bus stops per hour:
\[ \text{Time stopped (in minutes)} = \left( \frac{\text{Difference in speed}}{\text{Speed excluding stoppages}} \right) \times 60 \]
Substituting the values we have:
\[ \text{Time stopped} = \left( \frac{9}{54} \right) \times 60 \]

### Step 4: Simplify the fraction
Now, simplify the fraction:
\[ \frac{9}{54} = \frac{1}{6} \]
So we can rewrite the equation as:
\[ \text{Time stopped} = \left( \frac{1}{6} \right) \times 60 \]

### Step 5: Calculate the final result
Now, calculate the time:
\[ \text{Time stopped} = 10 \text{ minutes} \]

Thus, the bus stops for **10 minutes per hour**.