To solve the problem of finding the present ages of three persons given their sum and past age ratios, follow this structured approach:

1. Understand the Given Information
- The sum of the current ages of the three persons is 150 years.
- Ten years ago, their ages were in the ratio of 7:8:9.

2. Setting Up the Equation
- Let the ages of the three persons ten years ago be represented as:
- Person A: 7x
- Person B: 8x
- Person C: 9x
- Therefore, the sum of their ages ten years ago:
- \( 7x + 8x + 9x = 24x \)

3. Current Ages Calculation
- Their current ages will be:
- Person A: \( 7x + 10 \)
- Person B: \( 8x + 10 \)
- Person C: \( 9x + 10 \)
- The equation for their current ages summing up to 150 is:
- \( (7x + 10) + (8x + 10) + (9x + 10) = 150 \)

4. Simplifying the Equation
- Combine like terms:
- \( 24x + 30 = 150 \)
- Solve for \( x \):
- \( 24x = 150 - 30 \)
- \( 24x = 120 \)
- \( x = 5 \)

5. Finding Present Ages
- Substitute \( x = 5 \) back into the current age formulas:
- Person A: \( 7(5) + 10 = 35 + 10 = 45 \)
- Person B: \( 8(5) + 10 = 40 + 10 = 50 \)
- Person C: \( 9(5) + 10 = 45 + 10 = 55 \)

6. Conclusion
- The present ages of the three persons are:
- Person A: 45 years
- Person B: 50 years
- Person C: 55 years