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: NORCET 3 - 2022 (Shift-2)

Explanation

The problem is solved by setting up a linear equation based on the given ratio and future condition.
Let the present ages of Arun and Geeta be 4x and 3x, respectively.
Arun's age after 6 years is given as 26, which translates to the equation: 4x + 6 = 26.
Solving for x gives x = 5.
Geeta's present age is 3x, which is 3 * 5 = 15 years.

Option A: If Geeta's present age is 12 years (3x), then x would be 4. This would make Arun's present age 4x = 16 years. After 6 years, Arun's age would be 16 + 6 = 22 years, which contradicts the given information that his age will be 26.
Option C: If Geeta's present age is 19 years, it does not fit the 3x model derived from the 4:3 ratio, as 19 is not a multiple of 3. This indicates a calculation error or misunderstanding of the ratio concept.
Option D: If Geeta's present age is 25 years, it also does not fit the 3x model from the 4:3 ratio, as 25 is not a multiple of 3. This points to an incorrect calculation.

Visual 1: Flowchart - A flowchart showing the step-by-step process: 1. Define ages with variable 'x' (4x, 3x). 2. Set up the equation (4x + 6 = 26). 3. Solve for 'x'. 4. Calculate Geeta's age (3x).

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving age-related problems using ratios and linear equations as background academic context rather than a clinical decision trigger.
Accurate calculation is crucial in many fields, including medication dosage in nursing, where a small mathematical error can have significant consequences.
This type of ratio problem is foundational for understanding proportional reasoning, which is applied in various scientific and medical calculations.
What if the ratio was 3:4 instead? Then Arun's age would be 3x and Geeta's 4x. The equation would be 3x + 6 = 26. 'x' would be 20/3, and Geeta's age would be 4 * (20/3) = 80/3 or approximately 26.67 years, which is not among the options.

How to Approach the Question

First, identify the core information: the ratio of present ages (4:3) and a condition about a future age (Arun's age will be 26 in 6 years).
Represent the unknown present ages using a common variable 'x' based on the ratio. Let Arun's age be 4x and Geeta's age be 3x.
Translate the future age condition into a mathematical equation. Arun's age in 6 years is his present age (4x) plus 6, which equals 26. So, 4x + 6 = 26.
Solve this linear equation for 'x'.
Once 'x' is found, substitute its value back into the expression for Geeta's present age (3x) to find the final answer.
Double-check your calculation by plugging the calculated ages back into the problem's conditions to ensure they hold true.

Concept Tested & Keywords

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Practise the full NORCET 3 - 2022 (Shift-2)

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