In a 100 metres race A can give B 10 metres and C 28 metres. In the same race, B can give C—

Options

A. 18 metres
B. 20 metres
C. 27 metres
D. 9 metres

Answer

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

### Step 1: Understand the given information
- In a 100 meters race:
- A can give B 10 meters. This means when A finishes 100 meters, B has run only 90 meters.
- A can give C 28 meters. This means when A finishes 100 meters, C has run only 72 meters.

### Step 2: Establish the ratios
From the information:
- When A runs 100 meters, B runs 90 meters.
- When A runs 100 meters, C runs 72 meters.

This gives us the following ratios:
- A : B = 100 : 90
- A : C = 100 : 72

### Step 3: Find the ratio of B to C
To find out how much B can give C, we need to establish the ratio of B to C. We can use the ratios we have:

1. From A : B = 100 : 90, we can express B in terms of A:
\[ B = \frac{90}{100} A \]

2. From A : C = 100 : 72, we can express C in terms of A:
\[ C = \frac{72}{100} A \]

### Step 4: Set up the ratio of B to C
Now, we can find the ratio of B to C:
\[ \frac{B}{C} = \frac{\frac{90}{100} A}{\frac{72}{100} A} = \frac{90}{72} \]
This simplifies to:
\[ \frac{B}{C} = \frac{90}{72} = \frac{5}{4} \]

### Step 5: Determine how much B gives to C
Now, we need to find out how much B can give C in a 100 meters race. Since the ratio of B to C is 5:4, we can set up the following:
- If B runs 100 meters, we can find out how much C runs using the ratio:
\[ \text{If } B = 100, \text{ then } C = \frac{4}{5} \times 100 = 80 \text{ meters} \]

### Step 6: Calculate the distance B gives to C
To find out how much B gives to C, we subtract the distance C runs from the distance B runs:
\[ \text{Distance B gives to C} = 100 - 80 = 20 \text{ meters} \]

### Final Answer
B can give C **20 meters** in a 100 meters race.

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