If 8 men complete a work in 6 days, how many days will 4 men take?

Appeared in: JIPMER Pondicherry NO - 2022

Explanation

The relationship between the number of workers and the time taken to complete a fixed amount of work is one of inverse proportion.
This means if the number of workers is halved (from 8 to 4), the time required to complete the work will double (from 6 to 12 days).
Using the formula M₁ × D₁ = M₂ × D₂: (8 men × 6 days) = (4 men × D₂), which gives 48 = 4 × D₂, so D₂ = 12 days.

Option A: This would imply that fewer workers complete the job faster, which contradicts the principle of inverse proportion. This would be the answer if the workforce was doubled, not halved.
Option B: This suggests that the time taken is independent of the number of workers, which is illogical. Halving the workforce must increase the time taken.
Option C: This is an arbitrary number that does not follow the mathematical principle of inverse proportion.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving work and time problems using inverse proportion as background academic context rather than a clinical decision trigger.
Understanding inverse proportion is a fundamental mathematical skill applicable in various fields for resource and time management.
This concept helps in estimating project timelines, workforce planning, and understanding relationships where increasing one variable decreases another.
What if? If the question asked how many men are needed to complete the work in 2 days, the calculation would be (8 men × 6 days) / 2 days = 24 men.

How to Approach the Question

First, identify the type of problem. This is a 'work and time' problem.
Determine the relationship between the variables. Here, the number of men and the number of days are inversely proportional: more men mean fewer days.
Set up the formula for inverse proportion: M₁ × D₁ = M₂ × D₂.
Plug in the known values: M₁ = 8, D₁ = 6, M₂ = 4.
Solve the equation for the unknown variable (D₂): 8 × 6 = 4 × D₂, which simplifies to 48 = 4 × D₂.
Calculate the final answer: D₂ = 48 / 4 = 12.

Concept Tested & Keywords

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