Two trains starting at the same time from two stations 300 km apart and going opposite directions cross each other at a distance of 160 km from one of them the ratio of their speeds is:

Options

A. 7:8
B. 6:7
C. 16:15
D. 7:9

Answer

To solve the problem of finding the ratio of the speeds of two trains that cross each other while traveling in opposite directions, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**:
- We have two trains starting from two stations that are 300 km apart.
- They cross each other at a distance of 160 km from one station.

2. **Determine the Distances**:
- Let’s denote the two stations as P and Q.
- The distance from station P to the crossing point (R) is 160 km.
- Therefore, the distance from station Q to the crossing point (R) is:
\[ 300 \text{ km} - 160 \text{ km} = 140 \text{ km} \]

3. **Set Up the Ratio of Speeds**:
- Let the speed of the train from station P be \( v_1 \) and the speed of the train from station Q be \( v_2 \).
- The time taken by both trains to reach the crossing point is the same since they started at the same time.

4. **Use the Formula for Speed**:
- The formula for speed is:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
- Since the time is the same for both trains when they meet, we can set up the ratio of their speeds based on the distances they traveled:
\[ \frac{v_1}{v_2} = \frac{\text{Distance from P to R}}{\text{Distance from Q to R}} = \frac{160 \text{ km}}{140 \text{ km}} \]

5. **Simplify the Ratio**:
- Simplifying the ratio:
\[ \frac{v_1}{v_2} = \frac{160}{140} = \frac{16}{14} = \frac{8}{7} \]

6. **Conclusion**:
- The ratio of the speeds of the two trains is:
\[ v_1 : v_2 = 8 : 7 \]

### Final Answer:
The ratio of the speeds of the two trains is **8:7**.