If x : : y = 5/9 and y: z = 4/7 then x : y: z is:?

Appeared in: ESIC Nursing Officer -2019 (Shift -1)

Explanation

The core task is to find a continuous ratio x:y:z from two separate ratios, x:y and y:z.
The key is to make the common term 'y' equal in both ratios by finding the Least Common Multiple (LCM) of its values (9 and 4), which is 36.
The first ratio (5:9) is multiplied by 4 to get 20:36.
The second ratio (4:7) is multiplied by 9 to get 36:63.
Once 'y' is standardized to 36 in both, the ratios can be combined into a single continuous ratio: 20:36:63.

Option A: This option incorrectly calculates the ratios. It seems to have multiplied the first ratio by 6 (5x6=30, 6x6=36) and the second by an incorrect factor.
Option B: This option has the values for x and y swapped and uses an incorrect value for z.
Option D: This option correctly calculates the values for x, y, and z but incorrectly swaps the positions of y and z.

Visual 1: Flowchart: A flowchart illustrating the step-by-step process of combining two ratios with a common term. It would show: 1. Identify common term 'y'. 2. Find LCM of y's values. 3. Multiply each ratio to match the LCM. 4. Combine the adjusted ratios.

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, proficiency in quantitative aptitude, including ratios, is essential for passing the non-nursing sections of nursing recruitment exams.
Understanding ratios is a foundational mathematical skill that helps in various real-world calculations, including medication dosage adjustments, though those are typically done with stricter protocols.
What if the ratios were x:y = 9:5 and y:z = 7:4? The LCM of y's values (5 and 7) would be 35. The first ratio becomes 63:35, the second becomes 35:20. The final ratio would be 63:35:20.

How to Approach the Question

First, identify the two given ratios and the common variable between them. Here, the ratios are x:y and y:z, and the common variable is 'y'.
Note the values corresponding to the common variable in both ratios. Here, y corresponds to 9 in the first ratio and 4 in the second.
Calculate the Least Common Multiple (LCM) of these two values. The LCM of 9 and 4 is 36.
Convert each ratio into an equivalent ratio where the value of the common variable is equal to the LCM. Multiply the first ratio (5:9) by 4 to get 20:36. Multiply the second ratio (4:7) by 9 to get 36:63.
Once the common term is the same, combine the ratios to form the continuous ratio x:y:z, which is 20:36:63.
Finally, match your result with the given options.

Concept Tested & Keywords

QEJW6vtjEImlI7DNTKKawN

Practise the full ESIC Nursing Officer -2019 (Shift -1)

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