If a bus covers 195 km in 3 hours and a train covers 300 km in 4 hours, then the ratio of their speeds is

Options

A. 13 : 15
B. 15:13
C. 13:12
D. 12:13

Answer

To find the ratio of the speeds of the bus and the train, we will follow these steps:

### Step 1: Calculate the Speed of the Bus
The speed of the bus can be calculated using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
For the bus:
- Distance = 195 km
- Time = 3 hours

So, the speed of the bus is:
\[ \text{Speed of Bus} = \frac{195 \text{ km}}{3 \text{ hours}} = 65 \text{ km/h} \]

### Step 2: Calculate the Speed of the Train
Now, we will calculate the speed of the train using the same formula:
For the train:
- Distance = 300 km
- Time = 4 hours

So, the speed of the train is:
\[ \text{Speed of Train} = \frac{300 \text{ km}}{4 \text{ hours}} = 75 \text{ km/h} \]

### Step 3: Set Up the Ratio of Speeds
Now that we have the speeds of both the bus and the train, we can set up the ratio:
\[ \text{Ratio of Speeds} = \frac{\text{Speed of Bus}}{\text{Speed of Train}} = \frac{65 \text{ km/h}}{75 \text{ km/h}} \]

### Step 4: Simplify the Ratio
To simplify the ratio \( \frac{65}{75} \), we can divide both numbers by their greatest common divisor, which is 5:
\[ \frac{65 \div 5}{75 \div 5} = \frac{13}{15} \]

### Final Answer
Thus, the ratio of the speeds of the bus to the train is:
\[ \text{Ratio of Speeds} = 13 : 15 \]

---