In a 1000 m race, A beats B by 100 m , and in the same race, A beats C by 190 m. Find by what distance does B beat C in the same race ?

Options

A. 110 m
B. 90 m
C. 100 m
D. 120 m

Answer

To solve the problem step by step, let's break down the information given in the question:

1. **Understanding the Race**:
- A races against B and C in a 1000 m race.
- When A finishes the race (1000 m), B is at 900 m (since A beats B by 100 m).
- When A finishes the race (1000 m), C is at 810 m (since A beats C by 190 m).

2. **Finding the Distances**:
- When A finishes the race, B has run 900 m.
- When A finishes the race, C has run 810 m.

3. **Calculating the Distance B beats C**:
- To find out by what distance B beats C, we need to calculate the difference in the distances they covered when A finished the race:
\[ \text{Distance B beats C} = \text{Distance covered by B} - \text{Distance covered by C} \]
\[ \text{Distance B beats C} = 900 \, \text{m} - 810 \, \text{m} = 90 \, \text{m} \]

4. **Conclusion**:
- Therefore, B beats C by 90 meters in the same race.

### Final Answer:
B beats C by 90 meters.