They are two places X and Y 200 km apart from each other initially two person P and Q both are at 'X'.The speed of P is 20 km/h and speed of Q is 30 km/h later on they starts to move to and fro between X and Y.if they meet first time at a point M somewherre between X and Y then what is the distance travelled by P?

Options

A. 160 km
B. 150 km
C. 200 km
D. 210 km

Answer

To solve the problem, we need to determine the distance traveled by person P when they first meet at point M between locations X and Y.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Distance between X and Y = 200 km
- Speed of P = 20 km/h
- Speed of Q = 30 km/h

2. **Calculate the Ratio of Speeds:**
- The ratio of the speeds of P and Q is:
\[ \text{Speed ratio} = \frac{20}{30} = \frac{2}{3} \]

3. **Understanding the Distance Ratio:**
- Since they start at the same time and meet at point M, the ratio of the distances they travel will be the same as the ratio of their speeds.
- Therefore, if P travels a distance of 2 units, Q will travel a distance of 3 units.

4. **Total Units of Distance:**
- The total distance (200 km) can be divided into parts according to the speed ratio:
- Total units = 2 (for P) + 3 (for Q) = 5 units

5. **Calculate the Value of One Unit:**
- Since the total distance is 200 km, the value of one unit is:
\[ \text{Value of one unit} = \frac{200 \text{ km}}{5} = 40 \text{ km} \]

6. **Distance Traveled by P:**
- The distance traveled by P is 2 units:
\[ \text{Distance traveled by P} = 2 \times 40 \text{ km} = 80 \text{ km} \]

7. **Conclusion:**
- Therefore, the distance traveled by P when they meet for the first time at point M is **80 km**.