Ages (present ratio with past total): Three persons have present ages in the ratio 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages.

Introduction / Context:
Combining a present-day ratio with a past sum is a typical constraint-matching task. Represent present ages by a common multiplier and adjust backwards to match the past total, then return to present values.

Given Data / Assumptions:

• Present ages: 4x, 7x, 9x.
• Eight years ago: (4x − 8) + (7x − 8) + (9x − 8) = 56.

Concept / Approach:
Compute the past sum in terms of x and solve. The linearity of age changes ensures each person reduces by the same eight years, simplifying the algebra.

Step-by-Step Solution:

Verification / Alternative check:
Eight years ago they were 8, 20, and 28; the sum is 8 + 20 + 28 = 56 (✓). The present ratio 16 : 28 : 36 reduces to 4 : 7 : 9 (✓).

Why Other Options Are Wrong:
Other triplets either do not align to 4 : 7 : 9 or fail the past-sum condition after subtracting eight from each age.

Common Pitfalls:
Subtracting the total of 24 only once from one person rather than distributing −8 across all three individuals.

Final Answer:
16, 28, 36