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Let's solve these three questions one by one.

### Question 1: Circular path meeting point

Pankaj and Rohit are walking in opposite directions around a circular path of 600 m. Their speeds are 2.85 m/s and 5.4 km/h, respectively.

1. Convert 5.4 km/h to meters per second:
   \[
   5.4 \, \text{km/h} = \frac{5.4 \times 1000}{3600} = 1.5 \, \text{m/s}
   \]

2. The relative speed when they are walking in opposite directions is:
   \[
   \text{Relative speed} = 2.85 \, \text{m/s} + 1.5 \, \text{m/s} = 4.35 \, \text{m/s}
   \]

3. Time to meet for the first time:
   Since they are walking in opposite directions, they will meet when the combined distance they cover equals the length of the circular path, 600 meters.

   Time \( t \) is given by:
   \[
   t = \frac{\text{Distance}}{\text{Relative speed}} = \frac{600}{4.35} \approx 137.93 \, \text{seconds}
   \]

4. Convert time to minutes:
   \[
   t = \frac{137.93}{60} \approx 2.3 \, \text{minutes}
   \]

### Answer: They will meet for the first time after **2.3 minutes**.

---

### Question 2: Average of prime numbers between 32 and 69

The prime numbers between 32 and 69 are:
\[ 37, 41, 43, 47, 53, 59, 61, 67 \]

The average is calculated as:
\[
\text{Average} = \frac{37 + 41 + 43 + 47 + 53 + 59 + 61 + 67}{8} = \frac{408}{8} = 51
\]

### Answer: The average is **51**.

---

### Question 3: Work completion

Ram can complete the work in 15 days, Rohan in 25 days, and Rohit in 30 days.

- Work done by Rohan and Rohit together in 1 day:
  \[
  \frac{1}{25} + \frac{1}{30} = \frac{6 + 5}{150} = \frac{11}{150}
  \]

  In 2 days, Rohan and Rohit will complete:
  \[
  2 \times \frac{11}{150} = \frac{22}{150}
  \]

  Remaining work after 2 days:
  \[
  1 - \frac{22}{150} = \frac{128}{150}
  \]

- Work done by Rohan and Ram together in 1 day:
  \[
  \frac{1}{25} + \frac{1}{15} = \frac{3 + 5}{75} = \frac{8}{75}
  \]

  Time to complete the remaining work:
  \[
  t = \frac{\frac{128}{150}}{\frac{8}{75}} = \frac{128}{150} \times \frac{75}{8} = 8 \, \text{days}
  \]

Total days to complete the work:
\[
2 + 8 = 10 \, \text{days}
\]

### Answer: The work will be completed in **10 days**.

---

Do you want more details or have any questions on these solutions?

Here are 5 related questions:
1. How do you calculate relative speed for two objects moving in opposite directions?
2. What are prime numbers, and how can we find them within a given range?
3. What is the general formula for calculating the average of a set of numbers?
4. How do you calculate combined work when multiple people work together?
5. How does time relate to distance and speed in uniform motion?

### Tip: When dealing with speeds in different units, always convert them to the same unit before solving the problem.

In a circular path of 600 m, Pankaj and Rohit start walking in opposite directions from the same point at the speeds of 2.85 m/s and 5.4 km/h, respectively. After how many minutes will they meet for the first time? The average of all prime numbers between 32 and 69 is: Ram can complete a piece work in 15 days, Rohan in 25 days, and Rohit in 30 days. Rohan and Rohit worked together for 2 days and then Rohit was replaced by Ram. In how many days altogether was the work completed?

Learn how to solve problems involving relative speed, finding the average of prime numbers between 32 and 69, and calculating work completion time when multiple people work together. Detailed step-by-step solutions are provided, making this content suitable for students in Grades 9-12.

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