In a 800 m race around a stadium having the circumference of 200 m, the top runner meets the last runner on the 5th minute of the race. If the top runner runs at twice the speed of the last runner, what is the time taken by the top runner to finish the race ?

Options

A. A)20 min
B. B)15 min
C. C)10 min
D. D)5 min

Answer

To solve the problem step by step, we will analyze the information given and use it to find the time taken by the top runner to finish the race.

### Step 1: Understand the problem
We have a race of 800 meters around a stadium with a circumference of 200 meters. The top runner meets the last runner after 5 minutes. The top runner runs at twice the speed of the last runner.

### Step 2: Define the speeds
Let the speed of the last runner be \( v \) meters per minute. Therefore, the speed of the top runner will be \( 2v \) meters per minute.

### Step 3: Calculate the distance covered when they meet
They meet after 5 minutes. In this time:
- The distance covered by the last runner is \( 5v \) meters.
- The distance covered by the top runner is \( 5 \times 2v = 10v \) meters.

### Step 4: Determine the total distance covered
Since they are running on a circular track, the top runner will have completed multiple laps. The distance between them when they meet is equivalent to one lap (the circumference of the track), which is 200 meters.

The total distance covered by both runners when they meet can be represented as:
\[ \text{Distance covered by top runner} - \text{Distance covered by last runner} = 200 \text{ meters} \]
This can be expressed as:
\[ 10v - 5v = 200 \]
\[ 5v = 200 \]
Thus,
\[ v = 40 \text{ meters per minute} \]

### Step 5: Calculate the speed of the top runner
The speed of the top runner is:
\[ 2v = 2 \times 40 = 80 \text{ meters per minute} \]

### Step 6: Calculate the time taken to finish the race
The total distance of the race is 800 meters. The time taken by the top runner to finish the race can be calculated using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
Substituting the values:
\[ \text{Time} = \frac{800 \text{ meters}}{80 \text{ meters per minute}} = 10 \text{ minutes} \]

### Conclusion
The time taken by the top runner to finish the race is **10 minutes**.

---