One of the two buses completes a journey of 300 km in `7 1/2` hours and the other a journey of 450 km in 9 hours. The ratio of their average speeds is :

Options

A. 2:3
B. 3:4
C. 4:5
D. 8:9

Answer

To find the ratio of the average speeds of the two buses, we will follow these steps:

### Step 1: Calculate the average speed of the first bus.
- **Distance covered by the first bus**: 300 km
- **Time taken by the first bus**: 7 1/2 hours = 7.5 hours
- **Formula for speed**: Speed = Distance / Time

Using the formula:
\[ \text{Speed of first bus} = \frac{300 \text{ km}}{7.5 \text{ hours}} \]

Calculating this gives:
\[ \text{Speed of first bus} = \frac{300}{7.5} = 40 \text{ km/h} \]

### Step 2: Calculate the average speed of the second bus.
- **Distance covered by the second bus**: 450 km
- **Time taken by the second bus**: 9 hours

Using the formula:
\[ \text{Speed of second bus} = \frac{450 \text{ km}}{9 \text{ hours}} \]

Calculating this gives:
\[ \text{Speed of second bus} = \frac{450}{9} = 50 \text{ km/h} \]

### Step 3: Find the ratio of the average speeds of the two buses.
Now we have the speeds:
- Speed of the first bus = 40 km/h
- Speed of the second bus = 50 km/h

To find the ratio:
\[ \text{Ratio of speeds} = \frac{\text{Speed of first bus}}{\text{Speed of second bus}} = \frac{40}{50} = \frac{4}{5} \]

### Conclusion:
The ratio of their average speeds is **4:5**.

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