Ages (ratio changes in 3 years): The ratio of ages of A and B is 3 : 11. After 3 years the ratio becomes 1 : 3. Find the present ages of A and B.

Introduction / Context:
This is a classic ages problem featuring a present ratio that changes after a fixed time interval. The goal is to convert ratios into algebraic expressions and solve consistently for present ages.

Given Data / Assumptions:

• Present ratio A : B = 3 : 11.
• After 3 years, the ratio becomes 1 : 3.
• Ages increase linearly with time; no other constraints.

Concept / Approach:
Let present ages be A = 3x and B = 11x. After 3 years: A + 3 and B + 3. Enforce the future ratio (A + 3) / (B + 3) = 1 / 3 and solve for x. Then compute actual ages.

Step-by-Step Solution:

Verification / Alternative check:
After 3 years: A = 12, B = 36 → ratio 12 : 36 = 1 : 3, matching the condition.

Why Other Options Are Wrong:
They fail the future ratio test when advanced by 3 years.

Common Pitfalls:
Mixing present and future ratios or incorrectly assigning A and B to ratio parts; always map present ratio directly to 3x and 11x here.

Final Answer:
9 years, 33 years