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

   7:9

2. B

   6:7

3. C

   4:5

4. D

   5:6

Appeared in: NORCET 3 - 2022 (Shift-1)

Explanation

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• The problem is solved by first representing the current ages as 3x and 4x, based on the given 3:4 ratio.
• An equation is formed using the information from four years ago: (3x - 4) / (4x - 4) = 5/7.
• Solving this linear equation by cross-multiplication yields x = 8.
• Using x=8, the current ages are calculated as 24 (A) and 32 (B).
• Their ages four years from now will be 28 (A) and 36 (B).
• The simplified ratio of 28:36 is 7:9, found by dividing both numbers by their greatest common divisor, 4.

Why Other Options Were Wrong

• Option B: The ratio 6:7 would correspond to ages like 24 and 28, or 30 and 35. This result would stem from a calculation error when determining the future ages or simplifying the final ratio.
• Option C: The ratio 4:5 is not arithmetically derived from the problem's conditions. It might be confused with the initial ratio or result from a significant miscalculation.
• Option D: The ratio 5:6 is close to the past ratio of 5:7 but does not match the calculated future ratio. This likely arises from an error in adding the future years or simplifying the final numbers.

Related Visual

• Visual 1: No visual is required for this question type, as it is a mathematical problem requiring algebraic calculation.

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 ratios and linear equations as background academic context rather than a clinical decision trigger.
• This question tests quantitative aptitude and logical reasoning, which are essential skills for nurses.
• Problem-solving skills are crucial in clinical settings for tasks like medication dosage calculations, interpreting lab results, and managing patient care schedules.
• What if the ratio four years ago was 2:3 instead of 5:7? The equation would be 3(3x-4) = 2(4x-4), leading to 9x-12 = 8x-8, so x=4. The current ages would be 12 and 16, and future ages 16 and 20, making the future ratio 16:20, which simplifies to 4:5.

How to Approach the Question

• First, identify the knowns (current age ratio, past age ratio) and the unknown (future age ratio).
• Represent the current ages using a single variable 'x' (e.g., Age A = 3x, Age B = 4x).
• Create an algebraic equation based on the condition given for the past (e.g., 'four years ago').
• Solve this equation to find the value of 'x'.
• Use the value of 'x' to calculate the exact current ages.
• Calculate the future ages by adding the specified number of years.

Concept Tested & Keywords

• Concept Tested: Solving age-related word problems using ratios and linear equations.
• Stem keywords: ratio, ages, A and B, four years ago, four years from now
• Lead-in keywords: What will be the ratio

Question ID

QD4g9cgpQUqz_b5Iby5RUO

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