'A' can do 1/4 of a work in 6 days and 'B' can do 2/3 of the work in 12 days. In how many days both 'A' and 'B' together can do the work?

Appeared in: OSSSC Nursing Officer-2023

Explanation

The core task is to find the combined work rate of A and B to determine how long they take to finish a job together.
First, calculate the total time each person takes to complete the work alone. A takes 6 / (1/4) = 24 days. B takes 12 / (2/3) = 18 days.
Next, determine their individual daily work rates. A's rate is 1/24 of the work per day, and B's rate is 1/18 of the work per day.
Sum the individual rates to find the combined rate: 1/24 + 1/18. The LCM of 24 and 18 is 72. So, (3/72) + (4/72) = 7/72 of the work per day.
The time taken to complete the work together is the reciprocal of the combined rate: 1 / (7/72) = 72/7 days.
Converting 72/7 to a mixed fraction gives 10 with a remainder of 2, which is 10 2/7 days.

Option A: 4 days is incorrect. This value might be obtained by incorrectly manipulating the given numbers without following the proper work-rate calculation method.
Option B: 7 1/2 days (or 7.5 days) is incorrect. This could result from miscalculation, such as incorrectly finding the LCM or adding the fractions.
Option D: 12 days is the time it takes for B to complete only 2/3 of the work, not the time for both A and B to complete the entire work together.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Work and Time as background academic context rather than a clinical decision trigger.
This is a quantitative aptitude question designed to test logical and mathematical reasoning skills.
While not directly related to clinical practice, strong problem-solving skills are essential for nurses in managing time, resources, and patient care tasks efficiently.
What if? If A and B worked at the same rate, and each could do 1/2 the work in 9 days, how long would they take together? In that case, each takes 18 days alone. Their combined rate would be 1/18 + 1/18 = 2/18 = 1/9. They would take 9 days together.

How to Approach the Question

First, identify the fraction of work done and the time taken by each individual ('A' and 'B').
Use this information to calculate the total time each person would take to complete the entire work (1 whole unit) alone. For 'A': if 1/4 work takes 6 days, the whole work takes 6 * 4 = 24 days. For 'B': if 2/3 work takes 12 days, the whole work takes 12 * (3/2) = 18 days.
Convert these total times into individual work rates (work per day). The rate is the reciprocal of the time. A's rate = 1/24. B's rate = 1/18.
Add the individual rates to find their combined work rate: 1/24 + 1/18.
Find the least common multiple (LCM) of the denominators (24 and 18) to add the fractions. The LCM is 72. The combined rate is (3+4)/72 = 7/72.
The total time to complete the work together is the reciprocal of the combined rate. Time = 1 / (7/72) = 72/7 days.

Concept Tested & Keywords

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