A can do a work in 6 days and B in 9 days. How many days will both take together to complete the work?

HPSSC - 2015

Non Nursing Subjects

Hard

Appeared in: HPSSC - 2015

Explanation

The problem can be solved by calculating the combined work rate of individuals A and B.
A's one-day work is 1/6 of the total work. B's one-day work is 1/9 of the total work.
Their combined one-day work is the sum of their individual rates: 1/6 + 1/9.
To add the fractions, find the LCM of 6 and 9, which is 18. The combined rate is (3+2)/18 = 5/18 of the work per day.
The total time taken to complete the work is the reciprocal of the combined daily work rate, which is 18/5 or 3.6 days.

Option A: 5 days is incorrect. This value might be obtained by an incorrect calculation, possibly by averaging the days and adding a factor, like (6+9)/2 = 7.5. This method does not correctly represent the combined work rate.
Option C: 4 days is incorrect. This value is 3/5 of 9, or 9/10 of 6. It may result from a misapplication of the formula, perhaps by incorrectly multiplying or dividing the rates.
Option D: 3 days is incorrect. This might be a result of incorrectly averaging the work rates or simply dividing one of the numbers (e.g., 9/3 or 6/2). When working together, the time taken must be less than the time taken by the faster person (6 days), but this value is an arithmetic error.

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 how to calculate the combined efficiency and time taken when two individuals work together as background academic context rather than a clinical decision trigger.
This question assesses basic quantitative aptitude, a skill necessary for various competitive examinations, including those for nursing positions.
While not a direct clinical calculation, the logical reasoning and mathematical skills are foundational for tasks like medication dosage calculation, fluid intake/output monitoring, and data interpretation.
What if? If B could also complete the work in 6 days, their combined time would be (6 × 6) / (6 + 6) = 36 / 12 = 3 days. This shows that when efficiency is equal, the time taken is halved.

How to Approach the Question

First, identify the question as a 'Work and Time' problem.
Note the time each person takes individually: A takes 6 days, and B takes 9 days.
The most straightforward method is the LCM method. Find the LCM of 6 and 9, which is 18. Assume this is the total 'units' of work.
Calculate the 'efficiency' or work rate for each person: A's rate = 18 units / 6 days = 3 units/day. B's rate = 18 units / 9 days = 2 units/day.
Add their efficiencies to find the combined work rate: 3 + 2 = 5 units/day.
Finally, divide the total work by the combined efficiency to find the total time taken: 18 units / 5 units/day = 3.6 days.

Concept Tested & Keywords

Concept Tested: This question tests the concept of 'Work and Time' from quantitative aptitude, specifically how to calculate the combined efficiency and time taken when two individuals work together.
Stem keywords: work, 6 days, 9 days, together
Lead-in keywords: How many days

QkuXmZZR3ABaJmd_fK1LaA