If 4 persons can complete a work in 9 days, then in how many days will 6 persons complete the same work?

Appeared in: RML MAINS 2025

Explanation

The core principle is that the number of people and the time to complete a fixed amount of work are in inverse proportion.
This means if you increase the number of workers, the time taken to complete the work decreases.
The total work is constant, calculated as (Number of Persons) × (Number of Days).
Given: 4 persons take 9 days. Total work = 4 × 9 = 36 person-days.
To find the days (D) for 6 persons: 6 × D = 36, which gives D = 36 / 6 = 6 days.

Option A: If 6 people worked for 5 days, the total work done would be 6 × 5 = 30 person-days, which is less than the required 36 person-days.
Option C: If 6 people worked for 7 days, the total work done would be 6 × 7 = 42 person-days, which is more than the required 36 person-days.
Option D: This is the time taken by 4 people. Since the number of people has increased to 6, the time taken must decrease.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Inverse Proportion in Time and Work Problems as background academic context rather than a clinical decision trigger.
This type of question tests logical reasoning and basic mathematical skills, which are part of the general aptitude section in many nursing entrance exams.
Understanding inverse relationships is a fundamental analytical skill applicable in various contexts, not just mathematical problems.
For example, in healthcare, the number of available nurses and the time each nurse can spend per patient are often inversely related during a shift.

How to Approach the Question

Step 1: Identify the relationship between the variables. Here, the number of persons and the number of days are inversely proportional; as one goes up, the other goes down.
Step 2: Calculate the total amount of work required. Total Work = (Initial number of persons) × (Initial number of days).
Step 3: Set up the equation for the new scenario using the constant total work: (New number of persons) × (New number of days) = Total Work.
Step 4: Solve the equation for the unknown variable, which is the 'New number of days'.
Step 5: Perform a logic check. Since more people are working (4 -> 6), the time taken should be less than the original time (9 days). The answer, 6 days, is indeed less than 9.

Concept Tested & Keywords

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