A can give B a start of 20 metres and C a start of 39 metres in a walking race of 400 metres. How much can B give C a start ?

Options

A. 20 m
B. 15 m
C. 18 m
D. 25 m

Answer

To solve the problem, we need to determine how much of a start B can give C based on the information provided about A, B, and C's performance in a 400-meter race.

### Step-by-Step Solution:

1. **Understanding the Race Distances**:
- A can give B a start of 20 meters. This means when A runs 400 meters, B runs 380 meters (because B starts 20 meters behind).
- A can give C a start of 39 meters. This means when A runs 400 meters, C runs 361 meters (because C starts 39 meters behind).

2. **Setting Up Ratios**:
- From the first point, the ratio of A's distance to B's distance is:
\[ \frac{A}{B} = \frac{400}{380} = \frac{40}{38} = \frac{20}{19} \]
- From the second point, the ratio of A's distance to C's distance is:
\[ \frac{A}{C} = \frac{400}{361} \]

3. **Finding the Ratio of B to C**:
- We can express the ratio of B to C using the ratios we found:
\[ \frac{B}{C} = \frac{B}{A} \cdot \frac{A}{C} = \frac{380}{400} \cdot \frac{400}{361} = \frac{380}{361} \]

4. **Calculating the Start B Gives C**:
- To find out how much B can give C a start, we need to find out how much C runs when B runs 400 meters.
- Using the ratio \( \frac{B}{C} = \frac{380}{361} \):
\[ \text{If } B \text{ runs } 400 \text{ meters, then } C \text{ runs } \left( \frac{361}{380} \times 400 \right) \]
- Calculate the distance C runs:
\[ C \text{ runs } = \frac{361 \times 400}{380} = \frac{144400}{380} \approx 380 \text{ meters} \]

5. **Finding the Start**:
- The distance B gives C a start is the difference between the total distance and the distance C runs:
\[ \text{Start} = 400 - C \text{ distance} = 400 - 380 = 20 \text{ meters} \]

### Final Answer:
B can give C a start of **20 meters**.