Arun and Barun run with the speeds of 30 m/s and 20 m/s around a circular track of 600 m. They participate in a 3000 m race. What is the distance covered by Arun when he passes Barun for the 5th time?

Options

A. 2200 m
B. 2250 m
C. 2850 m
D. none of the above

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the time taken for Arun to pass Barun for the first time.

**Relative Speed Calculation:**
- Speed of Arun = 30 m/s
- Speed of Barun = 20 m/s
- Relative Speed = Speed of Arun - Speed of Barun = 30 m/s - 20 m/s = 10 m/s

**Time to Pass for the First Time:**
- Distance of the circular track = 600 m
- Time taken to pass Barun for the first time = Distance / Relative Speed = 600 m / 10 m/s = 60 seconds

### Step 2: Calculate the total distance Arun covers when he passes Barun for the fifth time.

**Total Time Calculation:**
- Since Arun passes Barun for the first time in 60 seconds, he will pass him for the fifth time in:
- Total time = 60 seconds * 5 = 300 seconds

### Step 3: Calculate the distance covered by Arun in that time.

**Distance Calculation:**
- Distance covered by Arun in 300 seconds = Speed of Arun * Time = 30 m/s * 300 s = 9000 m

### Conclusion:
The distance covered by Arun when he passes Barun for the 5th time is **9000 meters**.

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