Difficulty: Medium
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:
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
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