A quality control analyst rejects 0.08% of the fabric produced, finding it defective. How many meters of fabric must he examine to reject 4 meters?

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

Explanation

The problem states that 0.08% of a total quantity equals 4 meters.
To find the total quantity, we set up the equation: Total = Part / Percentage.
First, convert the percentage to a decimal: 0.08% = 0.08 / 100 = 0.0008.
Then, calculate the total: Total = 4 / 0.0008.
This calculation yields 5000 meters, which is the required total amount of fabric to be examined.

Option B: This value (2500) would be the answer if the defective rate was 0.16% (4 / 0.0016) or if a calculation error was made, such as dividing 40,000 by 16 instead of 8.
Option C: This value (10000) would be the answer if the defective rate was 0.04% (4 / 0.0004). This indicates a misinterpretation of the given percentage.
Option D: This value (1000) is incorrect and likely results from a significant decimal placement error, such as dividing 4 by 0.004 instead of 0.0008.

Visual 1: Infographic: A pie chart illustrating the relationship: Total Fabric (the whole pie) = Defective Fabric (a tiny 0.08% slice) + Non-Defective Fabric (the remaining 99.92% slice).
Visual 2: Flowchart: A simple diagram showing the steps: 1. Identify Part (4m) and Percentage (0.08%). 2. Convert Percentage to Decimal (0.0008). 3. Divide Part by Decimal (4 / 0.0008). 4. Arrive at Total (5000m).

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain This question tests the ability to solve percentage-based word problems, specifically finding the 'whole' when the 'part' and 'percentage' are given as background academic context rather than a clinical decision trigger.
This question assesses basic numeracy and problem-solving skills, which are foundational for a nursing career.
While not a clinical scenario, the same logical process is used in critical nursing tasks like medication dosage calculations, where a small error in understanding percentages can have serious consequences for patient safety.
For example, calculating drug concentrations (e.g., a 2% lidocaine solution) or interpreting lab results that are expressed as percentages requires this fundamental mathematical skill.

How to Approach the Question

First, carefully read the word problem to identify the given information and what is being asked. Here, you are given a 'part' (4 meters) and a 'percentage' (0.08%). You need to find the 'total'.
Recognize that this is a standard percentage problem where: (Percentage / 100) × Total = Part.
Convert the given percentage into a decimal or a fraction. It's often easier to work with decimals: 0.08% becomes 0.0008.
Set up the algebraic equation: 0.0008 × Total = 4.
Solve for the unknown variable ('Total') by rearranging the equation: Total = 4 / 0.0008.
Perform the final calculation and double-check your answer by plugging it back into the original problem statement to ensure it makes sense.

Concept Tested & Keywords

Concept Tested: This question tests the ability to solve percentage-based word problems, specifically finding the 'whole' when the 'part' and 'percentage' are given.
Stem keywords: quality control, rejects, fabric, defective
Lead-in keywords: How many

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