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

Introduction / Context:
We combine ratio information with a product of ages to find actual present ages, and then compute a future ratio after a fixed number of years. This is a straightforward algebraic setup using ratios.

Given Data / Assumptions:

• Father : Son = 4 : 1.
• Product of present ages = 196.
• Find ratio after 5 years.

Concept / Approach:
Represent the ages as 4x and x. Use the product 4x^2 = 196 to find x, compute present ages, add 5 to each, and take the ratio.

Step-by-Step Solution:
Let Father = 4x, Son = x. Product: 4x^2 = 196 ⇒ x^2 = 49 ⇒ x = 7. Present ages: Father = 28, Son = 7. After 5 years: Father = 33, Son = 12. Required ratio = 33 : 12 = 11 : 4.

Verification / Alternative check:
Recomputing the product with present ages: 28 * 7 = 196 (matches given). Future ratio calculation is consistent.

Why Other Options Are Wrong:
3 : 1 and 10 : 3 do not match 33 : 12. 14 : 5 incorrectly scales the ages after adding 5 years.

Common Pitfalls:
Using 196 as a sum rather than a product, or forgetting to add 5 to both ages before forming the final ratio.

Final Answer:
11 : 4