A can do a work in 4 days, B in 5 days and C in 10 days. Working together, they can do the work in?

Appeared in: RRB Staff Nurse Mumbai-2015

Explanation

The core principle is to find the fraction of work each person completes in one day (their work rate) and then sum these fractions to get the combined daily work rate.
A's daily work is 1/4, B's is 1/5, and C's is 1/10.
Their combined daily work is the sum of these rates: (1/4) + (1/5) + (1/10) = 11/20 of the job per day.
The total time taken to complete the job is the reciprocal of the combined daily work rate, which is 1 / (11/20) = 20/11 days.
Converting the improper fraction 20/11 to a mixed number gives 1 9/11 days.

Option A: This equals 5/3 days. This value might be obtained through an incorrect calculation of the LCM or an error in adding the fractions.
Option C: This equals 17/6 days. This is a plausible distractor but does not result from the correct summation of the work rates 1/4, 1/5, and 1/10.
Option D: This might be chosen by incorrectly averaging the days. A key logic check is that working together must result in a time less than the fastest individual's time (4 days), making 3 days a correct but not the exact answer.

Visual 1: Flowchart - A flowchart showing the steps: 1. Find individual daily work rates (1/T). 2. Sum the rates using LCM. 3. Take the reciprocal of the sum to find the total time.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating combined work rate and time as background academic context rather than a clinical decision trigger.
While not a clinical question, this type of logical reasoning is essential for nurses in tasks like resource management, time allocation for patient care, and managing workloads in a team setting.
This problem-solving skill helps in prioritizing tasks and estimating time for completion, which is crucial for efficient and safe patient care.
What if? If C was as fast as B (5 days), the combined work rate would be 1/4 + 1/5 + 1/5 = (5+4+4)/20 = 13/20. The time taken would be 20/13 days, or approximately 1.54 days, showing how team efficiency improves with faster members.

How to Approach the Question

Identify the question type: This is a 'Work and Time' problem.
Understand the core concept: If a person takes 'x' days to do a job, their work rate for one day is 1/x.
Calculate the individual one-day work rate for each person: A = 1/4, B = 1/5, C = 1/10.
Sum the individual rates to find the combined one-day work rate: (1/4) + (1/5) + (1/10).
Find the Least Common Multiple (LCM) of the denominators (4, 5, 10) to add the fractions. The LCM is 20.
Calculate the sum: (5/20) + (4/20) + (2/20) = 11/20. This is the fraction of work they do together in one day.

Concept Tested & Keywords

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