The present ages of two persons are 36 years and 50 years. After n years, the ratio of their ages will be 3 : 4. Find n.

Introduction / Context:
Set up a single equation in n using a future ratio of two known present ages, then solve directly.

Given Data / Assumptions:

• Person 1 now = 36; Person 2 now = 50
• (36 + n) : (50 + n) = 3 : 4

Concept / Approach:
Cross-multiply and solve for n, ensuring n is nonnegative and reasonable.

Step-by-Step Solution:

Verification / Alternative check:
After 6 years: ages 42 and 56 ⇒ 42 : 56 = 3 : 4, correct.

Why Other Options Are Wrong:
3, 4, 7 do not produce the required future ratio when substituted.

Common Pitfalls:
Reversing the ratio or adding n to only one age.

Final Answer:
6.