If 3.6 : 12.9 = 18 : x, find the value of x.

Appeared in: DSSSB 12 August 2024

Explanation

The problem presents a proportion, which is an equation stating that two ratios are equal.
The proportion 3.6 : 12.9 = 18 : x can be written in fractional form as 3.6/12.9 = 18/x.
To solve for the unknown variable 'x', the method of cross-multiplication is used. This means multiplying the numerator of the first fraction by the denominator of the second, and vice-versa: 3.6 * x = 12.9 * 18.
The product of 12.9 and 18 is 232.2, leading to the equation 3.6 * x = 232.2.
To isolate x, divide 232.2 by 3.6, which results in x = 64.5.

Option A: This value is incorrect. It would be obtained if there was an error in the division step (232.2 / 3.6).
Option B: This is an incorrect result. It likely arises from a miscalculation during the multiplication (12.9 * 18) or division step.
Option C: This value is close to the correct answer but is inaccurate. Such an error could happen due to rounding prematurely or a mistake in the long division process.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving proportions and finding the value of an unknown variable as background academic context rather than a clinical decision trigger.
Accurate calculation of ratios and proportions is a fundamental skill in nursing, critical for safe medication administration, especially when calculating drug dosages based on patient weight or preparing solutions.
This mathematical skill is also essential for calculating IV drip rates, converting units (e.g., lbs to kg), and ensuring the correct concentration of mixtures.
What if? If a nurse miscalculated a proportion for a potent medication like an anticoagulant or insulin, it could lead to a sub-therapeutic dose (risking treatment failure, like a blood clot) or an overdose (risking severe adverse effects, like major bleeding or hypoglycemia). This highlights the direct link between mathematical accuracy and patient safety.

How to Approach the Question

First, identify that the question presents a proportion in the format 'a : b = c : d'.
Convert this ratio notation into its equivalent fractional form: a/b = c/d. For this problem, it becomes 3.6/12.9 = 18/x.
Apply the rule of cross-multiplication, which states that for a proportion, the product of the extremes (a and d) is equal to the product of the means (b and c). This gives the equation: 3.6 * x = 12.9 * 18.
Calculate the product on the side of the equation with known values: 12.9 * 18 = 232.2.
Now, solve for the unknown variable 'x' by isolating it. Divide the product from the previous step by the coefficient of x: x = 232.2 / 3.6.
Perform the final division to find the value of x and select the matching option.

Concept Tested & Keywords

Concept Tested: Solving proportions and finding the value of an unknown variable.
Stem keywords: proportion, ratio, find the value of x
Lead-in keywords: find the value

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Practise the full DSSSB 12 August 2024

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