A, B, and C, when each works alone, can do a piece of work in 9 days, 12 days and 18 days, respectively. They all started the work together, but A and C both left after 3 days. In how many days was the total work completed?

Appeared in: RRB Nsg. Superintendent - 29 April 2025 (Shift-3rd)

Explanation

The core concept is to calculate work rate (the fraction of work done per day).
First, calculate the combined work rate of A, B, and C and find the amount of work they complete in 3 days.
The remaining work is then calculated by subtracting the completed work from the total work (which is 1 unit).
The time taken by B to finish the remaining work is found by dividing the remaining work by B's individual work rate.
The total time is the sum of the initial 3 days and the time B worked alone.

Option A: The value '3' represents only the initial period when A, B, and C worked together. It does not account for the additional time B took to finish the job.
Option B: The value '9/2' or 4.5 days is an incorrect calculation. It might result from miscalculating the remaining work or the time B took to complete it.
Option C: The value '9/5' or 1.8 days is an incorrect calculation. It does not align with any logical step in solving the problem.

Visual 1: Flowchart: A flowchart illustrating the two phases of the work: Phase 1 (A+B+C working for 3 days) and Phase 2 (B working alone to finish the rest), leading to the total time.

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 quantitative aptitude question designed to test logical reasoning and mathematical skills.
This type of problem is not directly related to clinical nursing practice but is a common component of competitive examinations to assess general intelligence and problem-solving abilities.
What if? - If the stem changed one defining clue so that 6 no longer matched, reassess the option whose mechanism, classification, or indication now fits the revised presentation.

How to Approach the Question

First, identify the time each person takes to complete the work individually. Convert this into their individual 'work rate' (the fraction of work done in one day). For A, the rate is 1/9; for B, 1/12; for C, 1/18.
Calculate the combined work rate when they work together by adding their individual rates.
Determine the amount of work completed during the time they worked together (3 days) by multiplying the combined rate by the number of days.
Calculate the remaining work by subtracting the completed work from 1 (representing the whole task).
Determine the time required for the remaining person (B) to finish the work by dividing the remaining work by that person's individual rate.
Finally, add the initial time (3 days) to the time taken by the last person to find the total time.

Concept Tested & Keywords

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Practise the full RRB Nsg. Superintendent - 29 April 2025 (Shift-3rd)

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