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)?

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:

  • 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

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