To solve this, let's analyze the given conditions:

1. Track Length: 900 meters.
2. Ratio of Speeds of A and B: 3 : 7.
3. They are running in opposite directions.

Let's break down the solution:

Step 1: Determine Individual Speeds

Since the ratio of their speeds is 3:7, we can represent A's speed as $3x$ and B's speed as $7x$, where $x$ is a common multiplier.

Step 2: Relative Speed

Since they are running in opposite directions, their relative speed will be the sum of their speeds: $3x + 7x = 10x$

Step 3: Time to Complete One Lap

Since they start at the same point and will meet for the first time at the starting point after both completing a full lap, we calculate the time it takes them to meet at the starting point again.

Since B's speed is faster, we’ll calculate based on the time A takes to complete the lap:

• Total distance = 900 meters.
• A’s speed = $3x$, so $\text{Time} = \frac{900}{3x} = 300/x$.

Thus, both A and B will meet at the starting point after $300/x$ seconds.

Step 4: Calculate Instances of 10m Distance

Since their relative speed is $10x$, the time taken to have a separation of 10 meters is: $\text{Time} = \frac{10}{10x} = \frac{1}{x} \text{ seconds}$

Within the total time of $300/x$ seconds, the number of times A and B are at a distance of 10 meters from each other is: $\frac{300/x}{1/x} = 300$

Thus, A and B will be at a distance of 10 meters from each other 300 times.

Since this answer is not in the options, let's verify if an adjustment is required based on problem constraints or typical errors in interpreting "distance times." Given the current structure, if an answer adjustment arises through simplification or clarifying meeting points only:

Conclusion: Final Answer Not Match