एक बस 3 घण्टे में 126 किमीo तथा एक ट्रेन 5 घण्टे में 315km दूरी तय करते है। बस तथा ट्रेन की चालों का अनुपात ज्ञात करो।

Options

A. `126:315`
B. `2:3`
C. `1:3`
D. `3:5`

Answer

To find the ratio of the speeds of the bus and the train, we will first calculate the speed of each vehicle and then find their ratio.

### Step 1: Calculate the speed of the bus
The formula for speed is:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
For the bus:
- Distance = 126 km
- Time = 3 hours

Using the formula:
\[ \text{Speed of bus} = \frac{126 \text{ km}}{3 \text{ hours}} = 42 \text{ km/h} \]

### 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 = 315 km
- Time = 5 hours

Using the formula:
\[ \text{Speed of train} = \frac{315 \text{ km}}{5 \text{ hours}} = 63 \text{ km/h} \]

### Step 3: Find the ratio of the speeds
Now we will find the ratio of the speed of the bus to the speed of the train.
\[ \text{Ratio} = \frac{\text{Speed of bus}}{\text{Speed of train}} = \frac{42 \text{ km/h}}{63 \text{ km/h}} \]

To simplify this ratio, we can divide both numbers by their greatest common divisor (GCD), which is 21:
\[ \text{Ratio} = \frac{42 \div 21}{63 \div 21} = \frac{2}{3} \]

### Final Answer
The ratio of the speeds of the bus to the train is \( \frac{2}{3} \).

---