A can work in 4 hours and B & C both can do this work in 3 hours. A and C can do this work in 2 hours, how many times B can this work alone?

Appeared in: AIIMS Rishikesh NO - 2019

Explanation

The problem is solved by first establishing the work rate for each individual or group as the fraction of work done per hour.
A's rate is 1/4 per hour, (B+C)'s rate is 1/3 per hour, and (A+C)'s rate is 1/2 per hour.
By subtracting A's rate from (A+C)'s rate, we find C's rate is 1/4 per hour.
Then, by subtracting C's rate from (B+C)'s rate, we find B's rate is 1/12 per hour.
The time taken for B to complete the work alone is the reciprocal of its rate, which is 1 / (1/12) = 12 hours.

Option A: This is the time taken for A and C to complete the work together, not the time for B alone.
Option B: This is the time taken for A to complete the work alone.
Option C: This value is mathematically incorrect and does not correspond to the time taken by any individual or group based on the given rates.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain This question tests the ability to solve problems related to work and time by calculating individual efficiencies from combined work rates as background academic context rather than a clinical decision trigger.
This question is not related to clinical nursing practice.
It assesses basic mathematical aptitude and logical reasoning, which are essential problem-solving skills for nurses in any setting.
For example, nurses use similar logical steps for tasks like calculating medication dosages or managing time-sensitive patient care schedules.

How to Approach the Question

First, understand that 'work rate' is the amount of work done in one unit of time. If someone takes 'T' hours to do a job, their rate is 1/T of the job per hour.
Translate the given information into equations: Rate(A) = 1/4, Rate(B) + Rate(C) = 1/3, Rate(A) + Rate(C) = 1/2.
Identify the goal: Find the time B takes alone, which means you need to find Rate(B).
Use the equations to solve for the unknown rates. Start by finding Rate(C) using the two equations that involve A and C: Rate(C) = (Rate(A) + Rate(C)) - Rate(A).
Once you have Rate(C), use the equation involving B and C to find Rate(B): Rate(B) = (Rate(B) + Rate(C)) - Rate(C).
Finally, calculate the time for B by taking the reciprocal of Rate(B): Time(B) = 1 / Rate(B).

Concept Tested & Keywords

Concept Tested: This question tests the ability to solve problems related to work and time by calculating individual efficiencies from combined work rates.
Stem keywords: work, hours, A, B, C, alone
Lead-in keywords: how many times

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