John started from A to B and Vinod from B to A. If the distance between A and B is 125 km and they meet at 75 km fromA,what is the ratio of John's speed to that of Vinod's speed?

Options

A. `2 :3`
B. `3 :2`
C. `4 :3`
D. `5 :4`

Answer

To solve the problem, we need to find the ratio of John's speed to Vinod's speed based on the distances they traveled before they met.

### Step-by-Step Solution:

1. **Identify the Total Distance**:
The total distance between points A and B is given as 125 km.

2. **Identify the Meeting Point**:
They meet at a point that is 75 km from A. This means John has traveled 75 km.

3. **Calculate the Distance Traveled by Vinod**:
Since the total distance is 125 km and John has traveled 75 km, the distance Vinod has traveled is:
\[ \text{Distance traveled by Vinod} = \text{Total Distance} - \text{Distance traveled by John} = 125 \text{ km} - 75 \text{ km} = 50 \text{ km} \]

4. **Set Up the Speed Ratio**:
Let John's speed be \( S_J \) and Vinod's speed be \( S_V \). Since they meet at the same time, we can use the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
Therefore, the time taken by both John and Vinod to meet can be expressed as:
\[ \text{Time taken by John} = \frac{75}{S_J} \quad \text{and} \quad \text{Time taken by Vinod} = \frac{50}{S_V} \]
Since they meet at the same time, we can equate the two:
\[ \frac{75}{S_J} = \frac{50}{S_V} \]

5. **Cross Multiply to Find the Ratio**:
Cross-multiplying gives us:
\[ 75 \cdot S_V = 50 \cdot S_J \]
Rearranging this gives:
\[ \frac{S_J}{S_V} = \frac{75}{50} = \frac{3}{2} \]

6. **Conclusion**:
The ratio of John's speed to Vinod's speed is:
\[ \text{Ratio of John's speed to Vinod's speed} = 3:2 \]