If X:Y=3:4 and Y:Z=5:6 then what is X:Z?

Appeared in: ESIC Nursing Officer 2016 (Shift -2)

Explanation

The problem requires finding a composite ratio from two individual ratios that share a common term (Y).
The most direct method is to express the ratios as fractions (X/Y and Y/Z) and multiply them.
Multiplying (X/Y) by (Y/Z) results in X/Z, as the common term 'Y' cancels out.
Calculation: (3/4) × (5/6) = 15/24.
The final step is to simplify the resulting ratio 15:24 by dividing both parts by their greatest common divisor (3), which yields 5:8.

Option A: The ratio 3:6 (or 1:2) is incorrect. It might arise from an arbitrary or incorrect combination of the numbers, such as taking the 'X' value (3) and the 'Z' value (6) directly from the given ratios without proper calculation.
Option B: The ratio 6:3 (or 2:1) is the inverse of the first incorrect option and does not follow the correct mathematical procedure for combining ratios.
Option D: The ratio 8:5 is the inverse of the correct answer. It represents the ratio of Z:X, not X:Z.

Visual 1: Infographic: A flowchart demonstrating the two methods to solve the problem. Method 1 shows (X/Y) * (Y/Z) = X/Z. Method 2 shows finding the LCM of the 'Y' terms, adjusting the ratios, and then combining them.

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.
This question tests fundamental quantitative aptitude and logical reasoning, skills that are essential for nurses.
Nurses frequently use ratios and proportions for tasks like calculating drug dosages, diluting solutions, and interpreting medical data.
For example, if a medication is available as 500 mg in 2 mL, a nurse uses ratios to determine how many mL to administer for a 250 mg dose.

How to Approach the Question

First, identify the information given: two separate ratios, X:Y = 3:4 and Y:Z = 5:6.
Next, identify what needs to be found: the combined ratio X:Z.
Recognize that the term 'Y' is the link between the two ratios.
Choose a method. Method 1: Convert ratios to fractions (X/Y = 3/4, Y/Z = 5/6) and multiply them to cancel out 'Y'.
Method 2: Make the 'Y' value the same in both ratios by finding the LCM of 4 and 5 (which is 20) and adjusting each ratio accordingly.
After calculating the combined ratio (15:24), always check if it can be simplified to its lowest terms (5:8).

Concept Tested & Keywords

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