15 years hence a man will be just 4 times as old as he was 15 years ago. His present age is -

Appeared in: AIIMS Delhi NO - 2017

Explanation

Let the present age be 'x'. The problem translates to the algebraic equation: x + 15 = 4 * (x - 15).
Solving the equation: x + 15 = 4x - 60, which simplifies to 3x = 75.
Dividing by 3 gives x = 25. Therefore, the man's present age is 25 years.
To verify, in 15 years, he will be 40. 15 years ago, he was 10. 40 is indeed 4 times 10, which matches the problem's condition.

Option A: If the present age is 10, his age 15 years ago would be 10 - 15 = -5 years, which is logically and physically impossible.
Option B: If the present age is 15, his age 15 years ago was 0. His age in 15 years will be 30. According to the problem, 30 should be 4 times 0, which is false (30 ≠ 0).
Option C: If the present age is 20, his age 15 years ago was 5. His age in 15 years will be 35. The condition requires his future age (35) to be 4 times his past age (5), but 35 is 7 times 5, not 4 times.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving age-related word problems using linear equations as background academic context rather than a clinical decision trigger.
This type of logical reasoning and mathematical problem-solving is a component of nursing entrance exams to assess a candidate's general aptitude and critical thinking skills.
These skills are foundational for clinical practice, especially for tasks like medication dosage calculations, interpreting lab results, and managing fluid balances.
What if the man was 3 times as old? The equation would become x + 15 = 3(x - 15), which simplifies to 2x = 60, resulting in a present age of 30 years.

How to Approach the Question

First, identify the unknown value the question asks for: the man's present age. Assign a variable to it, such as 'x'.
Translate the phrases from the word problem into mathematical expressions. '15 years hence' becomes 'x + 15', and '15 years ago' becomes 'x - 15'.
Construct an equation based on the relationship given: 'age in 15 years' is '4 times' 'age 15 years ago', so x + 15 = 4 * (x - 15).
Solve the linear equation for 'x' using standard algebraic steps (distribution, combining like terms, isolation of x).
Finally, check your answer by plugging the value of 'x' back into the original problem's conditions to ensure it holds true. This helps avoid calculation errors.

Concept Tested & Keywords

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Practise the full AIIMS Delhi NO - 2017

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