The present ages of three persons are in the ratio 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).

Problem restatementPresent ages are proportional to 4 : 7 : 9. Eight years ago their sum was 56. Determine each present age.

Given data

• Present-age ratio = 4 : 7 : 9.
• Eight years ago, sum of ages = 56.

Concept/ApproachLet present ages be 4k, 7k, 9k. Eight years ago, subtract 8 from each and use the given sum to solve for k.

Step-by-step calculation (4k − 8) + (7k − 8) + (9k − 8) = 56 20k − 24 = 56 20k = 80 → k = 4 Present ages = 4k, 7k, 9k = 16, 28, 36 (years)

Verification/AlternativeEight years ago: 8, 20, 28; sum = 56 (checks out). Ratio of present ages 16:28:36 reduces to 4:7:9.

Common pitfalls

• Forgetting to subtract 8 years from each person (subtracting only once from the total).

Final Answer16 years, 28 years, 36 years