Ages (difference now; past ratio given): The difference between the present ages of Arun and Barun is 14 years. Seven years ago, the ratio of their ages was 5 : 7. Find Barun's present age.

Introduction / Context:
This problem mixes a present absolute difference with a past ratio, a frequent pattern in age questions. The key is to express present ages from the ratio's time-slice and then align them with today's difference.

Given Data / Assumptions:

• Let present ages be A (Arun) and B (Barun), with B − A = 14 (Barun older, consistent with the 5 : 7 past ratio).
• Seven years ago: (A − 7) : (B − 7) = 5 : 7.

Concept / Approach:
Convert the past ratio into an equation and combine with the present difference. Solving the two linear equations yields today's ages directly.

Step-by-Step Solution:

Verification / Alternative check:
Seven years ago: A = 35, B = 49 ⇒ 35 : 49 = 5 : 7 (✓). Difference now 14 (✓).

Why Other Options Are Wrong:
All other listed numbers fail either the difference constraint or the reconstructed past ratio when checked.

Common Pitfalls:
Applying the 14-year difference to the past snapshot or reversing the elder–younger roles; the ratio 5 : 7 indicates Barun is older.

Final Answer:
56 years