The ratio of a father’s age to his son’s age is 4 : 1, and the product of their ages is 196. What will be the ratio of their ages after 5 years?

Introduction / Context:
Classic age problems often provide a ratio and the product (or sum). Use the ratio to write ages in terms of a variable, solve from the product, and then apply the time shift to compute the new ratio.

Given Data / Assumptions:

• Father : Son = 4 : 1 ⇒ ages = 4x and x.
• Product = 196 ⇒ 4x^2 = 196.
• We seek (4x + 5) : (x + 5).

Concept / Approach:
Solve x from the product, then add 5 years to each age and simplify the resulting ratio.

Step-by-Step Solution:

Verification / Alternative check:
Product check: 28×7 = 196; post-increment ratio simplifies correctly.

Why Other Options Are Wrong:
3:1, 10:3, or 14:5 do not match the computed post-increment ages.

Common Pitfalls:
Using 196 as the sum instead of product, or forgetting to simplify the final ratio.

Final Answer:
11 : 4