A and B can complete a work together in 9 days. If A alone can do it in 12 days, then, B alone can do one-third of the same work in ______ days.

Appeared in: RRB Nsg. Superintendent-2026 (Shift -3rd)

Explanation

The solution involves calculating the individual work rate (efficiency) for person B.
First, a total unit of work is assumed using the LCM of the given days (LCM of 9 and 12 is 36).
The combined efficiency of A and B is 4 units/day (36/9), and A's efficiency is 3 units/day (36/12).
By subtraction, B's efficiency is found to be 1 unit/day (4 - 3).
The work to be done is one-third of the total, which is 12 units (36/3).
Finally, the time taken by B is calculated by dividing the work (12 units) by B's efficiency (1 unit/day), which equals 12 days.

Option B: This is the time B would take to complete the entire work, not just one-third of it.
Option C: This value does not logically follow from the calculations based on the provided work rates and times.
Option D: This represents the time B would take to complete two-thirds of the work.

Visual 1: Flowchart: A flowchart illustrating the step-by-step process: 1. Find LCM for Total Work -> 2. Calculate Efficiencies of (A+B) and A -> 3. Subtract to find B's Efficiency -> 4. Calculate 1/3 of Total Work -> 5. Divide 1/3 Work by B's Efficiency to get Time.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Time and Work as background academic context rather than a clinical decision trigger.
This question assesses quantitative aptitude and logical reasoning, a non-nursing subject area often included in competitive nursing entrance exams to evaluate problem-solving skills.
While not directly related to clinical practice, the ability to perform systematic calculations is a foundational skill for tasks like medication dosage calculation and interpreting data.
What if the question asked for the time A and B would take to complete the work if B worked at half his efficiency? B's new efficiency would be 0.5 units/day. Combined efficiency would be 3 + 0.5 = 3.5 units/day. Time = 36 / 3.5 ≈ 10.3 days.

How to Approach the Question

Identify the question type: This is a 'Time and Work' problem from quantitative aptitude.
Recognize the given data: Time for (A+B) = 9 days, Time for A = 12 days.
Determine the goal: Find the time for B to complete 1/3 of the work.
Select a method: The LCM method is efficient. Assume total work as LCM of 9 and 12, which is 36 units.
Calculate the 'efficiency' (work per day) for each entity: Efficiency = Total Work / Time.
Use the efficiencies to find the unknown value (B's efficiency), and then calculate the final answer based on the specific amount of work required (one-third).

Concept Tested & Keywords

Concept Tested: Time and Work
Stem keywords: A and B, complete a work together, A alone, B alone, one-third of the same work
Lead-in keywords: in ______ days

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Practise the full RRB Nsg. Superintendent-2026 (Shift -3rd)

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