The ratio of the ages of A and B is 3:4. Four years ago , the ratio of their ages was 5:7 . What will be the ratio of the ages of A and B four years from now?

1. A

   5:6

2. B

   4:5

3. C

   6:7

4. D

   7:9

Appeared in: NORCET 2 - 2021 (shift-1)

Explanation

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• The solution involves setting up an algebraic equation based on the past age ratio to find a common multiplier, 'x'.
• First, represent the current ages as 3x and 4x. The condition four years ago gives the equation (3x - 4)/(4x - 4) = 5/7.
• Solving this equation yields x = 8. This allows for the calculation of the current ages as 24 and 32.
• Finally, the ages four years in the future will be 28 and 36, which simplifies to the ratio 7:9.

Why Other Options Were Wrong

• Option A: This ratio results from an incorrect calculation, possibly by miscalculating the future ages or simplifying the final ratio incorrectly.
• Option B: This is the current ratio of B's age to a hypothetical age of 40 (32:40 simplifies to 4:5). It does not represent the future ratio of A and B.
• Option C: This ratio might be obtained if there was a calculation error in finding the future ages or in the simplification step.

Related Visual

• Visual 1: Flowchart: A visual flowchart can illustrate the step-by-step process: 1. Define variables for current ages (3x, 4x). 2. Set up the equation for the past ages. 3. Solve for 'x'. 4. Calculate current ages. 5. Calculate future ages. 6. Simplify the final ratio.

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving age-based ratio and proportion problems using algebra as background academic context rather than a clinical decision trigger.
• This question tests quantitative aptitude and logical reasoning, which are essential skills for problem-solving in various professional fields, including healthcare administration and research.
• While not a direct clinical skill, the ability to perform accurate calculations is crucial for tasks like medication dosage, fluid balance monitoring, and interpreting lab results.
• What if the question asked for the ratio 8 years ago? The equation would be (3x-8)/(4x-8). The approach remains the same, but the specific values change, highlighting the importance of careful reading.

How to Approach the Question

• First, carefully read the problem to identify the knowns: the current age ratio (3:4) and a past age ratio (5:7, four years ago).
• Represent the current ages using a single variable (e.g., A's age = 3x, B's age = 4x).
• Use the information about the past to create an algebraic equation. In this case, (3x - 4) / (4x - 4) = 5/7.
• Solve this equation to find the value of the variable 'x'.
• Use the value of 'x' to calculate the actual current ages of A and B.
• Finally, calculate their ages at the future time specified (four years from now) and determine their simplified ratio.

Concept Tested & Keywords

• Concept Tested: Solving age-based ratio and proportion problems using algebra.
• Stem keywords: ratio, ages, four years ago, four years from now
• Lead-in keywords: What will be the ratio

Question ID

Q0-X8-BJkkARCPm2PGVmGk

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