A father and son together are 56 years old. In four years, the father’s age will be three times the son’s age. What are their present ages (son, father)?
Verbal Reasoning
Problems on Ages
Difficulty: Medium
Choose an option
-
A12 years, 44 years
-
B16 years, 40 years
-
C14 years, 42 years
-
D18 years, 38 years
-
ENone of these
Answer
Correct Answer: 12 years, 44 years
Explanation
Introduction / Context:Questions on ages often combine a present-time sum with a future (or past) ratio. Here, we are given the sum of a father’s and son’s ages now, and a relationship four years later. We must form linear equations and solve systematically.
Given Data / Assumptions:
- Present sum: father + son = 56 years.
- In 4 years: father will be three times the son then.
- All ages are whole-number years; relationships are exact.
Concept / Approach:Translate words into equations. Let s = son’s present age, f = father’s present age. Use simultaneous linear equations: f + s = 56 and (f + 4) = 3 * (s + 4).
Step-by-Step Solution:
Let s be the son’s present age and f be the father’s present age.Equation (1): f + s = 56.Equation (2): f + 4 = 3 * (s + 4) ⇒ f + 4 = 3s + 12 ⇒ f = 3s + 8.Substitute into (1): (3s + 8) + s = 56 ⇒ 4s + 8 = 56 ⇒ 4s = 48 ⇒ s = 12.Then f = 56 − 12 = 44.Verification / Alternative check:
In 4 years: son = 16, father = 48. Check 48 = 3 * 16 ✔.Why Other Options Are Wrong:
16,40: In 4 years, 44 ≠ 3 * 20.14,42: In 4 years, 46 ≠ 3 * 18.18,38: Sum is 56 but 42 ≠ 3 * 22/… fails future ratio.Common Pitfalls:
Mixing up “triple in 4 years” with “triple now.”Forgetting to add 4 years to both ages in the future condition.Final Answer:12 years, 44 years