If 5A = 4B, 7B = 3C and 2C = 7D, then B : D is

Appeared in: AIIMS CRE SNO - 2023

Explanation

The goal is to find the ratio B : D by linking the variables through the given equations.
From 7B = 3C, the ratio B/C is derived as 3/7.
From 2C = 7D, the ratio C/D is derived as 7/2.
To find B/D, multiply the two ratios: (B/C) × (C/D) = (3/7) × (7/2).
The common term 'C' effectively cancels out, as does the number '7', leaving the final ratio B/D = 3/2.

Option B: This is the inverse of the correct ratio (D : B). This error occurs if the final fraction is incorrectly inverted from 3/2 to 2/3 or if the initial ratios are set up incorrectly.
Option C: This ratio likely results from a calculation error, such as incorrectly multiplying or combining the numbers from the equations without following the rules of ratios.
Option D: This is the inverse of the ratio 6:5. Like the previous option, this is the result of a miscalculation and does not represent the correct relationship between B and D.

Visual 1: Flowchart: A flowchart illustrating the step-by-step process of solving chained ratio problems. It would show how to isolate individual ratios and then combine them to find the final desired ratio.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Ratio and Proportion as background academic context rather than a clinical decision trigger.
While not a clinical question, aptitude tests including mathematical reasoning are a common component of nursing entrance and recruitment exams.
This type of logical problem-solving assesses analytical skills that are valuable in clinical settings for tasks like interpreting data and calculating dosages.
What if the question asked for A : D? You would need to find A/B = 4/5, then calculate (A/B) × (B/C) × (C/D) = (4/5) × (3/7) × (7/2) = 12/10 = 6/5. The ratio A : D would be 6 : 5.

How to Approach the Question

First, identify all the given equations that relate the different variables (A, B, C, D).
Next, determine the specific ratio the question is asking for, which is B : D.
Identify the equations that link B to D. In this case, 7B = 3C and 2C = 7D are the relevant links. Notice that the equation 5A = 4B is extra information not needed to find B:D.
Convert each relevant equation into a ratio format. For example, convert 7B = 3C into B/C = 3/7.
Combine the intermediate ratios by multiplication to cancel out the linking variable (C). (B/D) = (B/C) × (C/D).
Substitute the numerical values and simplify the fraction to find the final ratio.

Concept Tested & Keywords

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Practise the full AIIMS CRE SNO - 2023

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