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

Appeared in: RRB Staff Nurse Ahmedabad-2015

Explanation

The fundamental principle is that if a person can complete a work in 'x' days, their work rate is 1/x of the work per day.
To find the combined work rate of multiple people, you add their individual work rates.
The total time taken to complete the work together is the reciprocal of their combined work rate.
A's rate is 1/4, B's is 1/5, and C's is 1/10. Their combined rate is 1/4 + 1/5 + 1/10 = 11/20.
The time taken is the reciprocal of the rate, which is 20/11 days, or 1 9/11 days.

Option A: This option, 1 3/5 days (or 8/5 days), is mathematically incorrect. It does not correspond to the reciprocal of the sum of the individual work rates.
Option C: This option, 2 5/6 days (or 17/6 days), is mathematically incorrect. The calculated time is 20/11 days, which is approximately 1.82 days, whereas 2 5/6 days is approximately 2.83 days.
Option D: This option, 3 days, is incorrect. It might be chosen by someone incorrectly averaging the days or making another conceptual error. The combined effort must result in a time shorter than the fastest individual's time (4 days).

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain This question tests the concept of 'Work and Time' from quantitative aptitude as background academic context rather than a clinical decision trigger.
This is a quantitative aptitude question designed to test mathematical reasoning and problem-solving skills, which are essential for various competitive exams.
While not directly clinical, the logical thinking and calculation skills honed by such problems are valuable for tasks like medication dosage calculations and interpreting patient data trends.
What if? - If the stem changed one defining clue so that 1 9/11 days no longer matched, reassess the option whose mechanism, classification, or indication now fits the revised presentation.

How to Approach the Question

First, identify the question as a 'Work and Time' problem.
Determine the work rate for each individual. The rate is the reciprocal of the time taken (e.g., if time is 'x' days, the rate is '1/x' of the work per day).
Calculate the combined work rate by adding the individual rates. This requires finding a common denominator for the fractions.
The total time taken to complete the work together is the reciprocal of the combined work rate.
Finally, convert the resulting improper fraction into a mixed number, as shown in the options, to find the correct answer.

Concept Tested & Keywords

Concept Tested: This question tests the concept of 'Work and Time' from quantitative aptitude.
Stem keywords: work, 4 days, 5 days, 10 days
Lead-in keywords: together can do the work in

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