Known present difference and past ratio: The difference between the current ages of a boss and his subordinate is 16 years. Four years ago, their ages were in the ratio 11 : 7 (Boss : Subordinate). Find the subordinate’s present age.

Introduction / Context:Combining a present absolute difference with a past-time ratio yields a solvable single-variable equation. Represent the boss as subordinate plus 16, then apply the ratio four years ago.

Given Data / Assumptions:

• Let subordinate now = s; boss now = s + 16.
• Four years ago: (s + 16 − 4) : (s − 4) = 11 : 7.

Concept / Approach:Set up (s + 12) / (s − 4) = 11 / 7 and solve for s.

Step-by-Step Solution:1) 7(s + 12) = 11(s − 4).2) 7s + 84 = 11s − 44.3) 128 = 4s ⇒ s = 32.4) Subordinate’s present age = 32 years.

Verification / Alternative check:Four years ago: subordinate 28, boss 44 ⇒ ratio 44 : 28 = 11 : 7 (correct). The present difference is 16, consistent.

Why Other Options Are Wrong:

• 28/36/40/30 do not satisfy both the difference and the ratio conditions upon verification.

Common Pitfalls:Not subtracting 4 from both ages, or flipping the ratio order, are typical errors.

Final Answer:32 years