Age-word problem — two conditions given: 15 years from now, A will be exactly twice as old as B. Five years ago, however, A was four times as old as B. Based on these two constraints, determine the difference between their present ages (A − B).

Introduction / Context:
Problems on ages often give two different time-based relations. Here, one relation is “15 years later” and the other is “5 years ago.” We must translate both into equations and solve simultaneously to get the present ages and then their difference.

Given Data / Assumptions:

• In 15 years: A will be twice B.
• Five years ago: A was four times B.
• All ages are in years; ages are integers in typical exam settings.

Concept / Approach:
Let present ages be A and B. Convert each statement into a linear equation in A and B and solve by elimination or substitution. Finally compute A − B.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 15 years, 45 years, 25 years do not satisfy both time-shift relations.
• “None of these” is incorrect because 30 years fits perfectly.

Common Pitfalls:

• Misplacing the time shifts (adding instead of subtracting).
• Computing A/B instead of the required difference A − B.

Final Answer:
30 years