Mohan and Sohan, together can do a job in 12 days. Sohan alone can do this job in 28 days. In how many days can Mohan alone do this job?

Appeared in: RRB Staff Nurse Kolkata-2015

Explanation

This problem is solved by calculating individual work rates, also known as efficiency.
The total amount of work is assumed to be the Least Common Multiple (LCM) of the given time periods. LCM of 12 and 28 is 84 units.
The combined efficiency of Mohan and Sohan is Total Work / Time = 84 / 12 = 7 units per day.
Sohan's individual efficiency is 84 / 28 = 3 units per day.
Mohan's efficiency is the difference between the combined efficiency and Sohan's efficiency: 7 - 3 = 4 units per day.
The time Mohan would take to complete the job alone is Total Work / Mohan's Efficiency = 84 / 4 = 21 days.

Option B: This is an incorrect answer. It is likely derived from simply subtracting the two given numbers (28 - 12 = 16). This is a common mistake, as time taken to do work cannot be directly added or subtracted; only work rates (efficiencies) can.
Option C: This is incorrect. This value does not result from the correct application of the work and time formulas. It may arise from a miscalculation of the LCM or individual efficiencies.
Option D: This is incorrect. Similar to the other distractors, this number does not align with the correct work-rate calculation and is included to test the candidate's accuracy.

Visual 1: Flowchart: A flowchart illustrating the LCM method for Work and Time problems. It would show the steps: 1. List given times. 2. Calculate LCM to find Total Work. 3. Calculate Combined and Individual Efficiencies. 4. Subtract efficiencies to find the unknown efficiency. 5. Divide Total Work by the unknown efficiency to find the 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 (Quantitative Aptitude) as background academic context rather than a clinical decision trigger.
This question tests quantitative aptitude and logical reasoning, which are foundational skills for nurses.
While not a direct clinical scenario, the ability to perform calculations accurately and follow a logical process is critical for tasks like drug dosage calculation, IV drip rate monitoring, and managing patient care schedules.
Many nursing recruitment and entrance exams include a general aptitude section to assess these fundamental problem-solving skills.

How to Approach the Question

First, identify the question as a 'Work and Time' problem from quantitative aptitude.
Recognize the given data: Time for (Mohan + Sohan) is 12 days, and Time for Sohan alone is 28 days. The goal is to find the time for Mohan alone.
Select an efficient method. The LCM method is ideal. Find the LCM of the time values (12 and 28) to represent the 'Total Work'. LCM(12, 28) = 84 units.
Calculate the 'efficiency' or 'work rate' for each given entity using the formula: Efficiency = Total Work / Time.
Calculate the combined efficiency: 84 / 12 = 7 units/day. Calculate Sohan's efficiency: 84 / 28 = 3 units/day.
Determine the unknown efficiency by subtraction: Mohan's Efficiency = Combined Efficiency - Sohan's Efficiency = 7 - 3 = 4 units/day.

Concept Tested & Keywords

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