Ages from ratio and product: The present age ratio of father and son is 7 : 4, and the product of their present ages is 1008. What will be their age ratio after 6 years?

Introduction / Context:
Given a ratio and a product, we find the common multiplier by taking the square root after factoring properly. Once current ages are known, adding 6 to both yields the future ratio.

Given Data / Assumptions:

• Father : Son = 7 : 4
• Product = 1008
• Find ratio after 6 years

Concept / Approach:
Let ages be 7x and 4x. Then 28x^2 = 1008 gives x. Compute current ages, add 6 to both, and simplify the ratio.

Step-by-Step Solution:

Verification / Alternative check:
Product check: 42 * 24 = 1008; ratio update is correct after equal increments of 6 years.

Why Other Options Are Wrong:
5 : 3 and 7 : 4 are not the future ratio; 5 : 8 reverses the order and is incorrect.

Common Pitfalls:
Forgetting that adding the same years to both changes the ratio unless both ages are equal initially.

Final Answer:
8 : 5