An error of 4% in excess is made while measuring each side of a square. What is the percentage of error in the calculated area of the square?

Appeared in: DSSSB - 29 August 2019 (Shift-1)

Explanation

Let the true side of the square be 's'. A 4% excess error means the measured side is 1.04s.
The area of a square is calculated by squaring its side length (Area = side²).
The new, calculated area is (1.04s)² = 1.0816s².
The error in area is the difference between the new area and the true area: 1.0816s² - s² = 0.0816s².
The percentage error is the error relative to the true area, multiplied by 100: (0.0816s² / s²) × 100 = 8.16%.

Option A: This value is incorrect. It seems to be a miscalculation, possibly derived from (1.02)², which would correspond to a 2% error in the side length, not 4%.
Option B: This is an arbitrary value with no clear mathematical relationship to the problem's parameters.
Option C: This is an arbitrary value with no clear mathematical relationship to the problem's parameters.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Percentage Error in Geometric Calculations as background academic context rather than a clinical decision trigger.
While not a clinical question, quantitative aptitude is a component of many nursing entrance and recruitment exams.
This type of problem tests logical reasoning and mathematical skills, which are essential for tasks like drug dosage calculations, where small measurement errors can lead to significant changes in the final dose.
What if? If the error was 4% in deficit (i.e., measured as too small), the measured side would be 0.96s. The new area would be (0.96s)² = 0.9216s². The percentage error would be a decrease of (1 - 0.9216) × 100 = 7.84%.

How to Approach the Question

First, identify the core task: calculating the percentage error in an area based on an error in a linear measurement.
Represent the initial error mathematically. A 4% excess means the new value is 104% of the original, or 1.04 times the original.
Write down the formula for the quantity being calculated (Area of a square = side²).
Substitute the new, erroneous measurement into the formula: New Area = (1.04 × side)².
Calculate the result: (1.04)² = 1.0816. The new area is 1.0816 times the original area.
Convert this factor into a percentage change. A factor of 1.0816 represents an 8.16% increase from the original value ( (1.0816 - 1) × 100 ).

Concept Tested & Keywords

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Practise the full DSSSB - 29 August 2019 (Shift-1)

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