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AIIMS Delhi NO - 2018
Quantitative Aptitude and Mathematics
Hard

The present ratio of ages of Arun and Geeta is 4:3. After 6 years, Arun’s age will be 26 years. What is the present age of Geeta?

Appeared in: AIIMS Delhi NO - 2018

Explanation

  • The present ages of Arun and Geeta are in the ratio 4:3, which can be represented as 4x and 3x, respectively, where 'x' is a common multiplier.
  • The problem states that Arun's age after 6 years will be 26. This gives the equation: 4x + 6 = 26.
  • Solving the equation for 'x': 4x = 20, which means x = 5.
  • Geeta's present age is 3x. Substituting the value of x, we get 3 * 5 = 15 years.

Why Other Options Were Wrong

  • Option A: If Geeta's age is 12 years (3x = 12), then x = 4. This would make Arun's present age 4x = 16. After 6 years, Arun would be 16 + 6 = 22, which contradicts the given information that he will be 26.
  • Option C: If Geeta's age is 19, it does not fit the 3x part of the ratio with an integer multiplier, making it inconsistent with the 4:3 ratio for whole years of age.
  • Option D: If Geeta's age is 25, it is not a multiple of 3, so it cannot be her present age based on the 4:3 ratio.

Related Visual

A flowchart illustrating the step-by-step process: 1. Set up ratio ages Arun \= 4x, Geeta \= 3x. 2. Formulate equation from the given condition 4x + 6 \= 26. 3. Solve the equat...
Clinical Relevance
  • Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving age-based word problems using ratios and linear equations as background academic context rather than a clinical decision trigger.
  • This type of problem tests logical reasoning and the ability to translate word problems into mathematical equations, a foundational skill for dosage calculations and interpreting data in a clinical setting.
  • Accuracy in calculation is critical. A small error in setting up or solving the equation leads to a completely different, incorrect answer.
  • What if? - If the question stated Arun's present age was 26, you would solve 4x = 26, find x = 6.5, and then calculate Geeta's age as 3 * 6.5 = 19.5 years.
How to Approach the Question
  • First, identify the key pieces of information: the ratio of present ages (4:3) and the future condition (Arun's age will be 26 in 6 years).
  • Represent the unknown present ages using a variable. Let Arun's age be 4x and Geeta's age be 3x.
  • Formulate a mathematical equation based on the future condition: 4x + 6 = 26.
  • Solve this linear equation to find the value of 'x'.
  • Once 'x' is found, substitute it back into the expression for Geeta's age (3x) to find the answer.
  • Finally, double-check your calculation and ensure the answer makes sense in the context of the problem.
Concept Tested & Keywords
  • Concept Tested: Solving age-based word problems using ratios and linear equations.
  • Stem keywords: ratio of ages, Arun, Geeta, 4:3, After 6 years, Arun’s age will be 26 years
  • Lead-in keywords: What is
  • Negative lead-in flag: false

Question ID

Q7_AyoC8maLwUKKFaiXdXR

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