If a: b is 3:4, b:c is 2:5, find a: b:c.?

Appeared in: DHS 2018 shift 1st

Explanation

The primary goal is to find a continuous ratio a:b:c from two separate ratios, a:b and b:c.
This requires making the value of the common term, 'b', consistent across both ratios.
The given ratios are a:b = 3:4 and b:c = 2:5. The values for 'b' are 4 and 2.
To equalize 'b', the second ratio (2:5) is multiplied by 2, resulting in a new ratio of 4:10.
With 'b' now equal to 4 in both ratios (a:b = 3:4 and b:c = 4:10), they can be combined to form a:b:c = 3:4:10.

Option B: This option (3:5:7) does not maintain the original proportions given in the problem. For example, a:b is 3:5 here, not 3:4.
Option C: This option (3:4:8) correctly identifies the a:b ratio but fails on the b:c ratio. A ratio of 4:8 simplifies to 1:2, not the required 2:5.
Option D: This option (3:2:9) incorrectly alters the first ratio a:b from 3:4 to 3:2. The integrity of both original ratios must be maintained.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Combining Ratios as background academic context rather than a clinical decision trigger.
While this is a mathematics question, strong numeracy skills are fundamental for safe nursing practice.
Nurses frequently use ratios and proportions for critical calculations, such as medication dosages, IV drip rates, and solution concentrations.
An inability to correctly manipulate ratios can lead to significant medication errors, posing a direct risk to patient safety.

How to Approach the Question

First, identify the two separate ratios provided in the question (a:b and b:c).
Identify the common element that links the two ratios. In this case, it is 'b'.
Look at the numerical values corresponding to the common element in both ratios (4 and 2).
Determine the least common multiple (LCM) for these values. The LCM of 4 and 2 is 4.
Adjust one or both ratios by multiplication to make the value of the common element equal to the LCM. Here, multiply the second ratio (2:5) by 2 to get 4:10.
Once the common element is equalized, combine the ratios into a single continuous ratio (a:b:c = 3:4:10) and select the matching option.

Concept Tested & Keywords

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Practise the full DHS 2018 shift 1st

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