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AIIMS Rishikesh & Jodhpur NO - 2017
Quantitative Aptitude and Mathematics
Hard

After 15 years, a man will be just 4 times as old as he was 15 years ago. What is his present age?

Appeared in: AIIMS Rishikesh & Jodhpur NO - 2017

Explanation

  • This question tests the ability to translate a word problem into a mathematical equation.
  • Let the present age be 'x'. The problem can be represented by the linear equation: x + 15 = 4(x - 15).
  • First, distribute the 4 on the right side: x + 15 = 4x - 60.
  • Next, isolate the variable 'x' by moving terms: 4x - x = 15 + 60, which simplifies to 3x = 75.
  • Solving for x gives x = 75 / 3, which equals 25.
  • Verification confirms the answer: 15 years from now he will be 40, and 15 years ago he was 10. 40 is indeed 4 times 10.

Why Other Options Were Wrong

  • Option A: If the present age is 10, his age 15 years ago would be 10 - 15 = -5, which is not possible.
  • Option B: If the present age is 20, his age after 15 years is 35, and his age 15 years ago was 5. 35 is 7 times 5, not 4 times.
  • Option C: If the present age is 15, his age 15 years ago was 0. The problem states his future age will be 4 times his past age, and 4 times 0 is 0, which doesn't match his future age of 30.

Related Visual

step guide showing how to translate the word problem After 15 years, a man will be 4 times as old as he was 15 years ago into the algebraic equation x + 15 \= 4x - 15 and t...
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.
  • While not a clinical question, this type of problem assesses logical reasoning and mathematical aptitude, which are essential skills for nurses.
  • Nurses frequently perform calculations for medication dosages, IV drip rates, and interpreting lab results, all of which require a foundation in mathematical principles.
  • What if the problem stated he would be 3 times as old? The equation would be x + 15 = 3(x - 15), leading to x + 15 = 3x - 45, then 2x = 60, and x = 30. The present age would be 30 years.
How to Approach the Question
  • First, carefully read the problem to identify the unknown quantity and the relationships between different quantities. Here, the unknown is the 'present age'.
  • Assign a variable to the unknown quantity. Let 'x' represent the present age.
  • Translate the phrases in the word problem into algebraic expressions. 'After 15 years' becomes 'x + 15', and '15 years ago' becomes 'x - 15'.
  • Formulate an equation that represents the relationship described in the problem: x + 15 = 4 * (x - 15).
  • Solve the linear equation for the variable 'x'.
  • Finally, verify your answer by substituting the value of 'x' back into the original problem statement to ensure it holds true.
Concept Tested & Keywords
  • Concept Tested: Solving age-related word problems using linear equations.
  • Stem keywords: present age, after 15 years, 15 years ago, 4 times as old
  • Lead-in keywords: What is

Question ID

QUdmmmZyCijUmYz2V3MkGp

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