If a bus travels 160 km in 4 hours and a train travels 320km in 5 hours at uniform speeds, then the ratio of the distances travelled by them in one hour is

Options

A. `1 : 2`
B. `4 : 5 `
C. `5 : 8 `
D. `8 : 5 `

Answer

To solve the problem, we need to determine the distances traveled by the bus and the train in one hour and then find the ratio of these distances.

### Step-by-Step Solution:

1. **Calculate the speed of the bus:**
- The bus travels 160 km in 4 hours.
- To find the distance traveled in one hour, we divide the total distance by the total time:
\[ \text{Speed of bus} = \frac{160 \text{ km}}{4 \text{ hours}} = 40 \text{ km/hour} \]

2. **Calculate the speed of the train:**
- The train travels 320 km in 5 hours.
- Similarly, we divide the total distance by the total time to find the distance traveled in one hour:
\[ \text{Speed of train} = \frac{320 \text{ km}}{5 \text{ hours}} = 64 \text{ km/hour} \]

3. **Set up the ratio of the distances:**
- Now we have the distances traveled by the bus and the train in one hour:
- Distance by bus = 40 km
- Distance by train = 64 km
- The ratio of the distances traveled by the bus to the train is:
\[ \text{Ratio} = \frac{\text{Distance by bus}}{\text{Distance by train}} = \frac{40}{64} \]

4. **Simplify the ratio:**
- To simplify \(\frac{40}{64}\), we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 8:
\[ \frac{40 \div 8}{64 \div 8} = \frac{5}{8} \]

5. **Final Answer:**
- The ratio of the distances traveled by the bus and the train in one hour is:
\[ 5 : 8 \]