A person P is at X and another person Q is atY. The distance between X and Y is 100 km. The speed of P is 20 km/h. While the speed of Q is 60 km/h?
If they first time meet at point Z somewhere between X and Y then the distance between X and Z is :

Options

A. 20 km
B. 40 km
C. 25 km
D. 30 km

Answer

To solve the problem, we need to determine the distance between point X and point Z, where persons P and Q meet.

### Step-by-Step Solution:

1. **Understand the Problem:**
- Person P starts at point X and moves towards point Y.
- Person Q starts at point Y and moves towards point X.
- The distance between X and Y is 100 km.
- Speed of P = 20 km/h
- Speed of Q = 60 km/h

2. **Calculate the Relative Speed:**
- Since both persons are moving towards each other, we can add their speeds to find the relative speed.
- Relative Speed = Speed of P + Speed of Q
- Relative Speed = 20 km/h + 60 km/h = 80 km/h

3. **Calculate the Time Taken to Meet:**
- To find the time taken for them to meet, we can use the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} \]
- Here, the distance is 100 km.
- Time = \( \frac{100 \text{ km}}{80 \text{ km/h}} = 1.25 \text{ hours} \)

4. **Calculate the Distance Covered by P:**
- Now, we can find out how far person P travels in that time.
- Distance = Speed × Time
- Distance covered by P = 20 km/h × 1.25 hours = 25 km

5. **Conclusion:**
- The distance between point X and point Z (where they meet) is 25 km.

### Final Answer:
The distance between X and Z is **25 km**.