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?
Verbal Reasoning
Problems on Ages
Difficulty: Easy
Choose an option
-
A3 : 1
-
B10 : 3
-
C11 : 4
-
D14 : 5
Answer
Correct Answer: 11 : 4
Explanation
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:
4x^2 = 196 ⇒ x^2 = 49 ⇒ x = 7 (ages positive).Father = 28, Son = 7.After 5 years: 33 and 12 ⇒ ratio = 33 : 12 = 11 : 4.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