In a 1000 m race, A beats B by 100 m and B beats C by 100 m. By how much distance can A beat C in the race ?

Answer

To solve the problem step by step, we will analyze the given information about the race between A, B, and C.

### Step 1: Understand the Race Conditions
- A beats B by 100 meters in a 1000-meter race. This means that when A finishes the race (1000 meters), B has only run 900 meters.

### Step 2: Determine B's Performance
- Since A beats B by 100 meters, we can conclude that when A runs 1000 meters, B runs 900 meters.

### Step 3: Analyze B's Race Against C
- Now, we know that B beats C by 100 meters as well. This means that when B finishes 1000 meters, C has only run 900 meters.

### Step 4: Relate A, B, and C's Distances
- From the previous steps, we can summarize:
- When A runs 1000 meters, B runs 900 meters.
- When B runs 900 meters, C runs 800 meters (because B beats C by 100 meters).

### Step 5: Calculate C's Distance When A Finishes
- We need to find out how far C runs when A runs 1000 meters.
- Since B runs 900 meters when A runs 1000 meters, and we know that C runs 800 meters when B runs 900 meters, we can conclude:
- When A runs 1000 meters, C runs 800 meters.

### Step 6: Determine the Distance A Beats C
- Now, we can find out how much distance A beats C by:
- Distance A beats C = Distance A runs - Distance C runs
- Distance A beats C = 1000 meters - 800 meters = 200 meters.

### Final Answer
- Therefore, A beats C by **200 meters** in the race.

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