A and B can do a job in 72 days. B and C can do the same job in 120 days, and A and C can do the same job in 90 days. In how many days will all the three take to complete the job?

Appeared in: RRB Staff Nurse Delhi-2015

Explanation

The core principle is to calculate the combined daily work rate of all three individuals (A, B, and C).
By summing the work rates of the pairs (1/72 + 1/120 + 1/90), we get the daily work of 2(A+B+C), which equals 1/30.
To find the daily work of just (A+B+C), we divide by 2, resulting in a work rate of 1/60.
The total time taken is the reciprocal of the daily work rate. Therefore, 1 / (1/60) equals 60 days.

Option A: 80 days is incorrect. This value may be obtained through a miscalculation, such as an error in finding the LCM of the denominators or incorrectly summing the fractions.
Option B: 100 days is incorrect. This likely stems from a calculation error, possibly in the final step of finding the reciprocal or during the addition of the work rates.
Option D: 150 days is incorrect. This answer might result from a conceptual misunderstanding, such as incorrectly averaging the times instead of correctly summing the work rates.

Visual 1: Flowchart - A flowchart illustrating the step-by-step process: 1. Convert days into daily work rates (1/Time). 2. Sum the work rates of the three pairs. 3. Note that this sum equals 2*(A+B+C)'s rate. 4. Divide the sum by 2 to find the combined rate of A+B+C. 5. Take the reciprocal of the result to find the total days.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain This question tests the concept of 'Work and Time' from quantitative aptitude, specifically problems involving the combined work rates of multiple individuals as background academic context rather than a clinical decision trigger.
While not a clinical question, this type of problem-solving assesses logical reasoning and mathematical aptitude, which are essential skills for nurses.
Nurses frequently perform calculations for medication dosages, IV drip rates, and patient intake/output, all of which require accuracy and a systematic approach similar to that used here.
What if the question asked for the time taken by A alone? You would first find the combined work rate of (A+B+C) as 1/60. Then, subtract the work rate of (B+C), which is 1/120. A's work rate would be 1/60 - 1/120 = 1/120, meaning A would take 120 days alone.

How to Approach the Question

First, identify that this is a 'Work and Time' problem where you are given the performance of pairs and asked for the performance of the group.
Convert the time taken by each pair into their 'one-day work' or 'work rate' by taking the reciprocal (e.g., 72 days becomes a rate of 1/72 per day).
Sum the work rates of the three pairs: (A+B) + (B+C) + (A+C). Recognize that this equals 2A + 2B + 2C, or 2(A+B+C).
Calculate the numerical sum of the fractions (1/72 + 1/120 + 1/90) by finding a common denominator (360).
Solve for the one-day work of (A+B+C) by dividing the sum by 2.
The final answer, the total time taken, is the reciprocal of this combined one-day work rate.

Concept Tested & Keywords

Concept Tested: This question tests the concept of 'Work and Time' from quantitative aptitude, specifically problems involving the combined work rates of multiple individuals.
Stem keywords: A and B, B and C, A and C, do a job, 72 days, 120 days, 90 days
Lead-in keywords: In how many days

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