A can give B a start of 15 m in a 100m race. B can give C a start of 10m in a 100m race. How much start can A give C in a 100m race?

Options

A. `33.5` metre
B. 25 metres
C. `23.5` metres
D. `28.5` metres

Answer

To solve the problem step by step, we need to analyze the relationships between A, B, and C based on the information given.

### Step 1: Understand the relationship between A and B
- A can give B a start of 15 meters in a 100-meter race.
- This means when A runs 100 meters, B runs 100 - 15 = 85 meters.

### Step 2: Understand the relationship between B and C
- B can give C a start of 10 meters in a 100-meter race.
- This means when B runs 100 meters, C runs 100 - 10 = 90 meters.

### Step 3: Set up the ratios
- From the first relationship, we know:
- A's distance = 100 meters
- B's distance = 85 meters
- From the second relationship, we know:
- B's distance = 100 meters
- C's distance = 90 meters

### Step 4: Find the equivalent distances for B
- To compare the two relationships, we need to express them in terms of the same distance for B. Let's set B's distance to 100 meters in both cases.
- For A and B:
- If B runs 100 meters, A runs (100/85) * 100 = 117.65 meters.
- For B and C:
- If B runs 100 meters, C runs (90/100) * 100 = 90 meters.

### Step 5: Establish the relationship between A and C
- Now we have:
- A runs 117.65 meters when B runs 100 meters.
- C runs 90 meters when B runs 100 meters.
- We can set up a ratio:
- A : C = 117.65 : 90

### Step 6: Calculate the distance C runs when A runs 100 meters
- To find out how much distance C covers when A runs 100 meters, we can set up a proportion:
- If A runs 117.65 meters, C runs 90 meters.
- If A runs 100 meters, C runs (90/117.65) * 100 = 76.65 meters.

### Step 7: Calculate the start A can give C
- The start that A can give C in a 100-meter race is:
- Start = 100 - C's distance when A runs 100 meters
- Start = 100 - 76.65 = 23.35 meters.

### Final Answer
A can give C a start of approximately **23.35 meters** in a 100-meter race.