If 8 workers complete a work in 15 days, then how many days will 10 workers take to complete the same work?

Appeared in: RML PRE 2025

Explanation

The problem demonstrates an inverse relationship between the number of workers and the time required to complete a task, assuming the total work remains constant.
The total work done is calculated as the product of the number of workers and the number of days, which is 8 workers × 15 days = 120 worker-days.
To find the new number of days for 10 workers, the total work (120 worker-days) is divided by the new number of workers (10), resulting in 12 days.
Alternatively, using the formula M₁D₁ = M₂D₂, we get 8 × 15 = 10 × D₂, which solves to D₂ = 12.

Option A: This is incorrect. It might be a result of a miscalculation or guessing. Increasing the workforce from 8 to 10 should decrease the time from 15 days, but not necessarily to 10 days.
Option C: This is incorrect. The time would remain 15 days only if the number of workers did not change. Since more workers are employed, the time taken must decrease.
Option D: This is incorrect. This implies that more workers take more time, which is a direct proportion. Work problems of this nature are based on inverse proportion.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Time and Work Problems as background academic context rather than a clinical decision trigger.
This question tests basic numeracy and logical reasoning, skills that are essential for various calculations in clinical practice, such as medication dosage, fluid balance, and staff scheduling.
While not a direct clinical scenario, the ability to perform such calculations quickly and accurately is a foundational skill for a nursing professional.
What if the question asked how many workers are needed to complete the work in 5 days? Using the same principle (120 worker-days / 5 days), you would find that 24 workers are needed.

How to Approach the Question

First, identify the given variables: initial workers (M₁ = 8), initial days (D₁ = 15), and new workers (M₂ = 10).
Recognize that the total amount of 'work' is constant. This means the relationship between the number of workers and the days they take is one of inverse proportion.
Recall or formulate the equation for inverse proportion: M₁ × D₁ = M₂ × D₂.
Substitute the known values into the equation: 8 × 15 = 10 × D₂.
Solve for the unknown variable, D₂: Calculate 120 = 10 × D₂, then divide 120 by 10 to get D₂ = 12.
Select the option that matches your calculated result.

Concept Tested & Keywords

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Practise the full RML PRE 2025

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