If 40 workers can complete a task in 6 days, in how many days will 60 workers complete the same task?

Appeared in: NHM UP Staff Nurse-2023 Shift-2nd

Explanation

The core concept is that the total work (measured in 'worker-days') is constant.
First, calculate the total work: 40 workers × 6 days = 240 worker-days.
This constant amount of work is then divided by the new number of workers to find the new time.
Time for 60 workers = 240 worker-days / 60 workers = 4 days.
This demonstrates an inverse relationship: as the number of workers increases, the time required to complete the task decreases.

Option A: This is incorrect. It might be chosen due to a calculation error, such as dividing 240 by 120 instead of 60.
Option B: This is incorrect. It could be the result of a miscalculation, perhaps dividing 240 by 80.
Option D: This is incorrect. It implies an extremely high number of workers.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Work and Time Problems (Inverse Proportion) as background academic context rather than a clinical decision trigger.
While not a clinical question, this type of logical reasoning is crucial for resource management and planning in any field, including healthcare.
For example, a nurse manager might use similar logic to determine staffing needs for a unit based on patient load and the time required for care tasks.
What if the question stated that the new workers work at half the pace? In that case, the effective number of new workers would be 30 (60 * 0.5), and the time taken would be 240 / 30 = 8 days.

How to Approach the Question

First, identify the variables given: initial workers (M₁) and initial days (D₁).
Recognize that the relationship between the number of workers and the time taken is inverse; more workers mean less time.
Calculate the total work required for the task by multiplying the initial workers by the initial days (Work = M₁ × D₁).
Set up the equation: Total Work = New Workers (M₂) × New Days (D₂).
Solve for the unknown variable (D₂), which is the new number of days.
Double-check your calculation and ensure the answer makes logical sense (i.e., more workers should result in fewer days).

Concept Tested & Keywords

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Practise the full NHM UP Staff Nurse-2023 Shift-2nd

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