A, B and C are three participants in 1 km race. If A can give B a start of 40 m and B can give C a start of 25 m, how many metres A can give C a start?

Answer

To solve the problem, we need to understand the relationships between the speeds of A, B, and C based on the given information.

### Step-by-step Solution:

1. **Understanding the Race Distances**:
- A can give B a start of 40 meters in a 1 km race. This means when A runs 1000 meters, B runs only 960 meters (1000 - 40 = 960).
- B can give C a start of 25 meters in a 1 km race. This means when B runs 1000 meters, C runs only 975 meters (1000 - 25 = 975).

2. **Finding the Speeds**:
- Let the speed of A be \( v_A \), the speed of B be \( v_B \), and the speed of C be \( v_C \).
- From the first relationship, we have:
\[ \frac{v_B}{v_A} = \frac{960}{1000} = \frac{24}{25} \]
- From the second relationship, we have:
\[ \frac{v_C}{v_B} = \frac{975}{1000} = \frac{39}{40} \]

3. **Finding the Ratio of Speeds**:
- To find the ratio of speeds between A and C, we can use the two ratios we have:
\[ \frac{v_C}{v_A} = \frac{v_C}{v_B} \cdot \frac{v_B}{v_A} = \frac{39}{40} \cdot \frac{24}{25} \]
- Now, we multiply these fractions:
\[ \frac{v_C}{v_A} = \frac{39 \times 24}{40 \times 25} = \frac{936}{1000} = \frac{117}{125} \]

4. **Calculating the Start A can give C**:
- If A runs 1000 meters, C would run:
\[ \text{Distance covered by C} = \frac{117}{125} \times 1000 = 936 \text{ meters} \]
- Therefore, the distance A can give C a start is:
\[ \text{Start given by A to C} = 1000 - 936 = 64 \text{ meters} \]

### Final Answer:
A can give C a start of **64 meters**.