A, B & C can do work in 15, 20 & 30 days. A works for whole time. Every third day B & C together work with A. The work is completed in how many days?

Appeared in: NHM MP Staff Nurse-2022

Explanation

The solution is found by first establishing a total unit of work using the LCM of the individual days (15, 20, 30), which is 60 units.
Individual work rates (efficiencies) are calculated: A=4, B=3, C=2 units/day.
The work is done in a 3-day cycle: Day 1 (A=4), Day 2 (A=4), Day 3 (A+B+C=9). Total work in one 3-day cycle is 17 units.
Three full cycles (9 days) complete 51 units of work, leaving 9 units remaining.
A works for the next two days (Day 10 and 11), completing 4+4=8 units, leaving 1 unit.
On the 12th day, A, B, and C work together (rate of 9 units/day) to complete the final 1 unit, which takes 1/9 of a day.

Option B: This value likely arises from a miscalculation of the work remaining after the full cycles or the time taken to complete it. For example, if one incorrectly calculated 7 units of work were left for the final day.
Option C: This value suggests an error in calculating the remaining work. It implies that only 2 units of work were left for the final day's group effort.
Option D: This value, which simplifies to 11 1/3, likely comes from a calculation error, possibly in summing the work done per cycle or the remaining work.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Work and Time problems involving cyclic work patterns as background academic context rather than a clinical decision trigger.
This question tests general aptitude and quantitative reasoning, which are essential skills for nurses.
Problem-solving and logical thinking are crucial for making sound clinical judgments and managing patient care effectively.
While not a clinical question, the ability to perform calculations accurately is vital in nursing for tasks like medication dosage calculation and IV drip rate monitoring.

How to Approach the Question

First, identify the type of problem: This is a 'Work and Time' problem with a cyclical work pattern.
Calculate the total amount of work by finding the Least Common Multiple (LCM) of the individual times (15, 20, 30).
Determine the rate of work (efficiency) for each person by dividing the total work by their individual time.
Analyze the work pattern: A works for 2 days, and then A, B, and C work together on the 3rd day. Calculate the total work done in one complete 3-day cycle.
Divide the total work by the work done per cycle to find how many full cycles are completed and how much work remains.
Calculate the time taken to complete the remaining work by following the work pattern day by day.

Concept Tested & Keywords

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Practise the full NHM MP Staff Nurse-2022

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