Question

A racecourse is 400 metres long. A and B run a race and A wins by 5 metres. B and C run over the same course and B wins by 4 metres. C and D run over it and D wins by 16 metres. If A and D run over it, then who would win and by how much?

• A. A, by 8.4 metres
• B. D, by 8.4 metres
• C. D, by 7.2 metres
• D. A, by 7.2 metres

Answer 1

The Correct Option is C

The correct option is (C): D, by 7.2 metres
Let's break down the problem step by step to explain why **D wins by 7.2 meters** over A:
Race 1: A vs B
- A wins by 5 meters in a 400-meter race.
- This means that when A finishes the 400 meters, B has run only 395 meters.

Thus, the speed ratio of A to B is:
\[\text{Speed of A} : \text{Speed of B} = 400 : 395\]

Race 2: B vs C
 B wins by 4 meters, meaning when B finishes the 400 meters, C has run 396 meters.

Thus, the speed ratio of B to C is:
\[\text{Speed of B} : \text{Speed of C} = 400 : 396\]

Race 3: C vs D
 D wins by 16 meters, meaning when D finishes the 400 meters, C has run 384 meters.

Thus, the speed ratio of C to D is:
\[\text{Speed of D} : \text{Speed of C} = 400 : 384\]

To find the result of the race between A and D:
We need to calculate the speed ratio of A to D by combining the ratios from the previous races.

1. A to B: \( \frac{400}{395} \)
2. B to C: \( \frac{400}{396} \)
3. D to C: \( \frac{400}{384} \)

Now, multiplying these ratios to get A to D:
\[\frac{\text{Speed of A}}{\text{Speed of D}} = \frac{400}{395} \times \frac{400}{396} \times \frac{384}{400}\]

This gives us the speed ratio of A to D. Using this ratio, we can calculate the difference in distance when both A and D run the 400-meter race.

After calculations, D wins the race by 7.2 meters over A.