A man is 24 years older than his son. In 2 years, his age will be twice the age of his son. Find the present age of son ?

Appeared in: HPSSC - 2015

Explanation

Let the son's present age be 'x'. The man's present age is 'x + 24'.
In 2 years, the son's age will be 'x + 2' and the man's age will be '(x + 24) + 2' which is 'x + 26'.
The problem states that in 2 years, the man's age will be twice the son's age, which gives the equation: x + 26 = 2(x + 2).
Solving the equation: x + 26 = 2x + 4, which simplifies to 22 = x.
Therefore, the son's present age is 22 years.

Option A: If the son's present age is 14, the man's age is 14 + 24 = 38. In 2 years, the son will be 16 and the man will be 40. Here, 40 is not twice 16 (40 ≠ 2 × 16).
Option B: If the son's present age is 18, the man's age is 18 + 24 = 42. In 2 years, the son will be 20 and the man will be 44. Here, 44 is not twice 20 (44 ≠ 2 × 20).
Option C: If the son's present age is 20, the man's age is 20 + 24 = 44. In 2 years, the son will be 22 and the man will be 46. Here, 46 is not twice 22 (46 ≠ 2 × 22).

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving linear equations from word problems involving ages as background academic context rather than a clinical decision trigger.
This question does not test a clinical nursing concept but rather assesses logical reasoning and mathematical aptitude.
Basic mathematical skills are essential for nurses for tasks like calculating drug dosages, infusion rates, and interpreting patient data, making aptitude tests a common part of nursing entrance exams.
What if the question stated the man's age would be three times the son's age in 2 years? The equation would change to x + 26 = 3(x + 2), leading to a different answer (x = 10).

How to Approach the Question

First, carefully read the problem to identify the unknowns and the relationships between them.
Assign a variable, typically 'x', to one of the unknown quantities. In this case, let the son's present age be 'x'.
Express the other unknown quantities in terms of 'x' based on the information given (e.g., Man's present age = x + 24).
Formulate expressions for their ages at the future time point mentioned in the problem (e.g., In 2 years, Son's age = x + 2, Man's age = x + 26).
Set up an algebraic equation based on the condition that relates their future ages (e.g., x + 26 = 2 * (x + 2)).
Solve the linear equation for 'x' to find the value of the unknown.

Concept Tested & Keywords

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Practise the full HPSSC - 2015

Attempt every question from this paper in a timed mock, then review the full solution for each one.