NORCET 6 mains-2024: A can do a work in 4 days, B can do it in 5 days and C can do it in 10 days, then A, B, C together can do the…

NORCET 6 mains-2024

Quantitative Aptitude and Mathematics

Hard

Appeared in: NORCET 6 mains-2024

Explanation

The problem requires calculating the total time taken for three individuals (A, B, and C) to complete a task when working together.
The most effective method is to determine the combined rate of work by summing their individual rates.
Using the LCM method, the total work is assumed to be the LCM of the days (4, 5, 10), which is 20 units.
The individual efficiencies (work per day) are A: 20/4=5, B: 20/5=4, and C: 20/10=2 units/day.
Their combined efficiency is 5 + 4 + 2 = 11 units/day.
The time taken together is Total Work / Combined Efficiency = 20 / 11 days, which simplifies to the mixed fraction 1 9/11 days.

Option A: This option, 1 5/3 days, is an improperly written mixed fraction because the fractional part (5/3) is greater than 1. It correctly converts to 1 + (1 and 2/3) = 2 2/3 days, which is not the calculated answer.
Option C: This value is the result of an incorrect calculation. A logical check shows that when people work together, the time taken must be less than the time taken by the fastest person (A, who takes 4 days). 2 5/6 days is a plausible but incorrect result.
Option D: This is an incorrect calculation. It might be a guess or the result of a significant error in summing the work rates.

Visual 1: Flowchart - Illustrates the LCM method for solving Work and Time problems: 1. Find LCM of days to get Total Work. 2. Calculate individual efficiency (Work/Days). 3. Sum efficiencies. 4. Calculate Total Time (Total Work / Combined Efficiency).

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Work and Time Problems as background academic context rather than a clinical decision trigger.
This is a general aptitude question testing mathematical reasoning, a fundamental skill required for various competitive exams, including those for nursing positions.
The underlying concept of calculating combined effort and efficiency is analogous to resource management in a clinical setting, such as determining staffing needs based on patient acuity and the number of available nurses.
What if? If C was as fast as B (taking 5 days), the LCM of (4, 5, 5) would still be 20. The efficiencies would be A=5, B=4, C=4. The combined efficiency would be 13 units/day, and the time taken would be 20/13 or 1 7/13 days.

How to Approach the Question

First, identify the question type as a mathematical problem on 'Work and Time'.
List the time taken by each individual to complete the work: A = 4 days, B = 5 days, C = 10 days.
Choose a method to solve. The LCM method is often the quickest.
Calculate the LCM of the given days (4, 5, 10), which is 20. This represents the 'total units of work'.
Determine the 'efficiency' (work rate) for each person by dividing the total work by their time (e.g., A's efficiency = 20/4 = 5 units/day).
Sum the individual efficiencies to find the combined efficiency when they work together.

Concept Tested & Keywords

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