A can give 40 m start to B and 70 m to C in a race of 1 km. How many metres start can B give to C in a race of 1 km?

Answer

To solve the problem step by step, we will analyze the information given and use it to find out how many meters start B can give to C in a race of 1 km.

### Step 1: Understand the given information
- A can give B a start of 40 meters in a 1000 meters (1 km) race.
- A can give C a start of 70 meters in the same 1000 meters race.

### Step 2: Determine the effective distances for B and C
- If A runs 1000 meters, B runs \(1000 - 40 = 960\) meters.
- If A runs 1000 meters, C runs \(1000 - 70 = 930\) meters.

### Step 3: Find the ratio of speeds of B and C
- The distance covered by B when A covers 1000 meters is 960 meters.
- The distance covered by C when A covers 1000 meters is 930 meters.
- Thus, the ratio of the speeds of B and C can be expressed as:
\[ \text{Speed of B : Speed of C} = 960 : 930 \]
- Simplifying this ratio:
\[ \text{Speed of B : Speed of C} = \frac{960}{930} = \frac{32}{31} \]

### Step 4: Calculate the start B can give to C in a 1 km race
- In a race of 1000 meters, we need to find how much distance B can give as a start to C.
- Let the distance that B can give to C be \(x\) meters.
- When B runs 1000 meters, C runs:
\[ \text{Distance covered by C} = \frac{31}{32} \times 1000 = 968.75 \text{ meters} \]
- Therefore, the start that B can give to C is:
\[ x = 1000 - 968.75 = 31.25 \text{ meters} \]

### Final Answer
B can give C a start of **31.25 meters** in a race of 1 km.

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