In a 100 metres race, A can beat B by 25 metres and B can beat C by 4 metres. In the same race, A can beat C by—

Options

A. 29 metres
B. 21 metres
C. 28 metres
D. 26 metres

Answer

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

### Step 1: Understand the race between A and B
- In a 100 meters race, A can beat B by 25 meters. This means that when A finishes the race (100 meters), B has only covered 75 meters.

**Calculation**:
- Distance covered by B when A covers 100 meters = 100 - 25 = 75 meters.

### Step 2: Understand the race between B and C
- B can beat C by 4 meters. This means that when B finishes the race (100 meters), C has only covered 96 meters.

**Calculation**:
- Distance covered by C when B covers 100 meters = 100 - 4 = 96 meters.

### Step 3: Establish the relationship between A and C
- We need to find out how much A can beat C by. To do this, we can use the relationships we established between A and B, and B and C.

### Step 4: Set up the ratios
- We can set up the ratios of the distances covered:
- A's distance to B's distance: \( \frac{A}{B} = \frac{100}{75} = \frac{4}{3} \)
- B's distance to C's distance: \( \frac{B}{C} = \frac{100}{96} = \frac{25}{24} \)

### Step 5: Combine the ratios
- To find the ratio of A to C, we multiply the two ratios:

\[ \frac{A}{C} = \frac{A}{B} \times \frac{B}{C} = \frac{4}{3} \times \frac{25}{24} \]

### Step 6: Calculate the combined ratio
- Now we calculate:

\[ \frac{A}{C} = \frac{4 \times 25}{3 \times 24} = \frac{100}{72} \]

### Step 7: Determine the distance C covers when A covers 100 meters
- When A covers 100 meters, we can find out how much C covers:

\[ C = \frac{72}{100} \times 100 = 72 \text{ meters} \]

### Step 8: Calculate how much A beats C by
- Finally, to find out how much A beats C by, we subtract the distance covered by C from the distance covered by A:

\[ \text{Distance A beats C by} = 100 - 72 = 28 \text{ meters} \]

### Final Answer
A can beat C by **28 meters**.

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