In 1 km race, the ratio of the speeds of two contestants L and M is 3 :4. L has a start of 280 m. Then, L wins by how many metres?

Options

A. 40 M
B. 60 M
C. 45 M
D. 65 M

Answer

To solve the problem, we need to determine how many meters L wins by in a 1 km race against M, given their speed ratio and L's head start.

### Step-by-Step Solution:

1. **Understand the Race Distance**:
- The total distance of the race is 1 km, which is equal to 1000 meters.

2. **Calculate the Effective Distance for L**:
- Since L has a head start of 280 meters, the distance L needs to cover to finish the race is:
\[ \text{Distance covered by L} = 1000 \text{ m} - 280 \text{ m} = 720 \text{ m} \]

3. **Use the Speed Ratio**:
- The ratio of the speeds of L and M is given as 3:4. This means that for every 3 meters L runs, M runs 4 meters.

4. **Determine the Distance M Covers in the Same Time**:
- If L covers 720 meters, we can find out how far M would cover in the same time.
- Let’s denote the distance M covers when L covers 720 meters. Since the speed ratio is 3:4, we can set up the proportion:
\[ \frac{L's \, distance}{M's \, distance} = \frac{3}{4} \]
- Let \( x \) be the distance M covers. Then:
\[ \frac{720}{x} = \frac{3}{4} \]
- Cross-multiplying gives:
\[ 3x = 720 \times 4 \]
\[ 3x = 2880 \]
\[ x = \frac{2880}{3} = 960 \text{ m} \]

5. **Calculate the Winning Margin**:
- Now that we know M covers 960 meters when L finishes, we can find out how far L wins by:
\[ \text{Winning Margin} = \text{Total Distance} - \text{Distance covered by M} \]
\[ \text{Winning Margin} = 1000 \text{ m} - 960 \text{ m} = 40 \text{ m} \]

### Final Answer:
L wins by **40 meters**.

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