A can run 40 m while B runs 50 m. In a km race, B beats A by which of the following distances?

Options

A. 175 m
B. 225 m
C. 335 m
D. 200 m

Answer

To solve the problem, we need to determine by how much distance B beats A in a 1 km race based on their running capabilities.

### Step-by-Step Solution:

1. **Understand the Given Information:**
- A runs 40 meters while B runs 50 meters.
- This means that in the same time, B covers more distance than A.

2. **Determine the Ratio of Distances:**
- The ratio of the distances run by A and B is 40:50, which simplifies to 4:5.
- This means for every 4 meters A runs, B runs 5 meters.

3. **Calculate the Distance B Beats A in a 50-meter Race:**
- In a race of 50 meters (the distance B runs), we need to find out how far A has run.
- Since the ratio is 4:5, if B runs 50 meters, A would run:
\[ \text{Distance run by A} = \left(\frac{4}{5}\right) \times 50 = 40 \text{ meters} \]
- Therefore, B beats A by:
\[ \text{Distance B beats A} = 50 - 40 = 10 \text{ meters} \]

4. **Scale Up to a 1 km Race:**
- Now, we need to find out how much B would beat A in a 1 km race (1000 meters).
- Since we know that in a 50-meter race, B beats A by 10 meters, we can scale this up.
- To find out how many times 50 meters fits into 1000 meters:
\[ \text{Number of 50-meter races in 1000 meters} = \frac{1000}{50} = 20 \]
- Therefore, in a 1 km race, B would beat A by:
\[ \text{Total distance B beats A} = 10 \text{ meters} \times 20 = 200 \text{ meters} \]

5. **Conclusion:**
- In a 1 km race, B beats A by **200 meters**.

### Final Answer:
B beats A by **200 meters**.

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