Points A, B, C and D lie on the same straight line such that B, C and D are 200 m, 300 m and 500 m away from A respectively. Anshu and Ravi leave A at the same time and run towards D. Simultaneously; Sindhu leaves D and runs towards A. Sindhu meet Anshu at C, and Ravi at B. If each person is running in uniform speed, then the speed of the fastest person is what percent more than that of the slowest person?

Let the speeds of Anshu, Ravi, and Sindhu be denoted by \( v_A \), \( v_R \), and \( v_S \), respectively.

### Step 1: Determine distances between points
- Points A, B, C, and D are collinear.
- Distances from A:
  - Distance from A to B = 200 m
  - Distance from A to C = 300 m
  - Distance from A to D = 500 m

### Step 2: Analyze the situation
- Anshu and Ravi start from point A and run towards point D.
- Sindhu starts from point D and runs towards point A.
- Sindhu meets Anshu at point C (300 m from A).
- Sindhu meets Ravi at point B (200 m from A).

Since all three are running at uniform speeds, the time taken for Sindhu to meet Anshu at C must be equal for both Anshu and Sindhu. Similarly, the time taken for Sindhu to meet Ravi at B must also be equal for both Ravi and Sindhu.

### Step 3: Establish relationships between distances and speeds
Let the time taken by Sindhu to meet Anshu at C be \( t_1 \) and the time taken to meet Ravi at B be \( t_2 \).

#### For Anshu and Sindhu:
- Distance traveled by Anshu to reach C = 300 m
- Distance traveled by Sindhu to reach C = 500 m - 300 m = 200 m

Using the relationship \( \text{distance} = \text{speed} \times \text{time} \), we get:
\[
v_A \cdot t_1 = 300
\]
\[
v_S \cdot t_1 = 200
\]
Dividing these two equations:
\[
\frac{v_A}{v_S} = \frac{300}{200} = \frac{3}{2}
\]
Thus, \( v_A = \frac{3}{2} v_S \). 

#### For Ravi and Sindhu:
- Distance traveled by Ravi to reach B = 200 m
- Distance traveled by Sindhu to reach B = 500 m - 200 m = 300 m

Similarly, we have:
\[
v_R \cdot t_2 = 200
\]
\[
v_S \cdot t_2 = 300
\]
Dividing these two equations:
\[
\frac{v_R}{v_S} = \frac{200}{300} = \frac{2}{3}
\]
Thus, \( v_R = \frac{2}{3} v_S \).

### Step 4: Find the ratio of the fastest speed to the slowest speed
Now, we compare the speeds:
- \( v_A = \frac{3}{2} v_S \)
- \( v_R = \frac{2}{3} v_S \)
- \( v_S = v_S \)

The fastest speed is \( v_A \) and the slowest speed is \( v_R \). To find what percentage \( v_A \) is more than \( v_R \), we calculate:
\[
\frac{v_A - v_R}{v_R} \times 100 = \frac{\frac{3}{2} v_S - \frac{2}{3} v_S}{\frac{2}{3} v_S} \times 100
\]
Simplifying:
\[
= \frac{\frac{9}{6} v_S - \frac{4}{6} v_S}{\frac{4}{6} v_S} \times 100
= \frac{\frac{5}{6} v_S}{\frac{4}{6} v_S} \times 100
= \frac{5}{4} \times 100 = 125\%
\]

Thus, the speed of the fastest person (Anshu) is **125%** more than that of the slowest person (Ravi).

Would you like more details on any part of the solution?

### Related Questions:
1. How can we calculate the speed of Sindhu based on given conditions?
2. If the distances were changed, how would it affect the final percentage?
3. What would happen if all three individuals had the same speed?
4. How would the result change if Ravi met Sindhu at a different point?
5. What if Sindhu met Anshu at a different location than point C?

**Tip:** Understanding the concept of relative speed can simplify solving problems involving multiple moving objects.

Points A, B, C and D lie on the same straight line such that B, C and D are 200 m, 300 m and 500 m away from A respectively. Anshu and Ravi leave A at the same time and run towards D. Simultaneously; Sindhu leaves D and runs towards A. Sindhu meets Anshu at C, and Ravi at B. If each person is running in uniform speed, then the speed of the fastest person is what percent more than that of the slowest person?

Learn how to calculate the percentage difference between the fastest and slowest runners based on their uniform speeds. This problem involves ratios, relative speed, and uniform motion concepts, suitable for Grades 9-11 students.

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