If 6 nursing officers can complete the physical stock verification of a ward inventory in 4 hours, how many hours will it take 8 nursing officers to complete the exact same task?

1. A

   3 hours

2. B

   2 hours

3. C

   5 hours

4. D

   4.5 hours

Appeared in: NORCET 8 Prelims-2025

Explanation

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• This problem demonstrates an inverse relationship: as the number of workers increases, the time taken to complete a fixed amount of work decreases.
• The total work required is constant and can be calculated as 6 officers × 4 hours = 24 officer-hours.
• To find the new time, divide the total work by the new number of officers: 24 officer-hours / 8 officers = 3 hours.
• The inverse proportion formula (N₁ × T₁ = N₂ × T₂) confirms this: 6 × 4 = 8 × T₂, which solves to T₂ = 3.

Why Other Options Were Wrong

• Option B: This answer is incorrect. For it to take 2 hours, the total work would need to be 16 officer-hours (8 officers × 2 hours), but the actual work is 24 officer-hours.
• Option C: This is incorrect because it implies a direct proportion. Increasing the number of workers should decrease the time, not increase it.
• Option D: This is incorrect as it also suggests a direct relationship. More workers should lead to a shorter completion time, not a longer one.

Related Visual

• Visual 1: Infographic. A simple chart showing the inverse relationship between the number of workers and the time taken to complete a fixed task. One side shows 6 people and 4 hours, the other shows 8 people and 3 hours, with the total 'work units' (24) remaining the same.
• Visual 2: Formula Card. A visual card displaying the inverse proportion formula N₁ × T₁ = N₂ × T₂ with each variable clearly defined.

Clinical Relevance

• Nursing practice connection: Knowing Inverse Proportion (Work-Rate Problem) helps nurses interpret findings accurately and avoid errors in routine assessment, medication administration, and patient teaching.
• This type of calculation is relevant to nursing management for efficient staff allocation. Nurse managers must often estimate the time and personnel required for tasks like ward audits, setting up new units, or managing patient admissions.
• Understanding work-rate principles helps in creating fair and balanced duty rosters, ensuring that workload is distributed evenly and tasks are completed within necessary timeframes.
• This skill is crucial for resource management, helping to justify staffing levels and plan for periods of high activity or staff shortages.

How to Approach the Question

• First, identify the relationship between the quantities. In this case, the number of officers and the time to complete the task are inversely proportional.
• Calculate the total amount of work. This is a constant value, found by multiplying the initial number of workers by the initial time (6 officers × 4 hours = 24 officer-hours).
• Use the total work constant to find the unknown variable. Divide the total work by the new number of workers to find the new time (24 officer-hours / 8 officers).
• Perform the calculation: 24 / 8 = 3 hours.
• Finally, check if the answer is logical. Since the number of officers increased from 6 to 8, the time taken should decrease from 4 hours. The answer, 3 hours, is logical.

Concept Tested & Keywords

• Concept Tested: Inverse Proportion (Work-Rate Problem)
• Stem keywords: nursing officers, physical stock verification, 6 officers, 4 hours, 8 officers
• Lead-in keywords: how many hours
• Clinical cues: The care setting changes urgency, monitoring level, and the expected nursing action.
• Negative lead-in flag: false

Question ID

Qg2ZmpTtuqDgAyVBsGdmWS

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