22 men can complete a job in 16 days. Then how many days will it take for 32 men to complete that job?

Appeared in: SGPGI Nursing Officer-2022

Explanation

The core principle is that the total work (measured in man-days) is constant.
First, calculate the total work: 22 men × 16 days = 352 man-days.
Then, divide the total work by the new number of men to find the new time: 352 man-days / 32 men = 11 days.
This demonstrates the inverse relationship: as the number of men increases from 22 to 32, the time required decreases from 16 to 11 days.

Option A: This is a result of an incorrect calculation and does not follow the precise inverse relationship between workers and time.
Option C: This value represents the original number of men, not the time required for the new group of men. It is a distractor that repeats a number from the problem statement.
Option D: This would be the correct time (8 days) only if the number of workers was doubled from 22 to 44, as the time would be halved (16 / 2 = 8). It applies an incorrect ratio.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain This question tests the mathematical concept of work and time, specifically focusing on inverse proportion as background academic context rather than a clinical decision trigger.
While not a clinical question, this type of problem assesses basic numeracy and logical reasoning skills.
These skills are essential for nurses in various tasks, such as calculating medication dosages, managing fluid intake/output, and interpreting patient data.
What if? If the number of men was halved to 11 instead of increased, the time taken would double. The calculation would be (22 × 16) / 11 = 32 days, demonstrating the inverse relationship in the other direction.

How to Approach the Question

First, identify the relationship between the variables. In this case, the number of men and the number of days are inversely proportional – as one increases, the other decreases.
Recall or write down the formula for inverse proportion: M₁ × D₁ = M₂ × D₂.
Plug in the known values from the question: M₁=22, D₁=16, M₂=32.
The equation becomes: 22 × 16 = 32 × D₂.
Solve the equation for the unknown variable, D₂.
Perform the calculation: D₂ = (22 × 16) / 32 = 11.

Concept Tested & Keywords

Concept Tested: This question tests the mathematical concept of work and time, specifically focusing on inverse proportion.
Stem keywords: men, complete a job, days
Lead-in keywords: how many days

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Practise the full SGPGI Nursing Officer-2022

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