A's efficiency is twice that of B. If both work together, they can complete the work in 16 days. In how many days can B alone complete the same work?

Appeared in: CGHS SSC - 2018

Explanation

The problem is solved by establishing a ratio of efficiency between A and B.
Let B's rate of work be 'x' units per day. Therefore, A's rate of work is '2x' units per day.
Their combined rate of work is x + 2x = 3x units per day.
The total amount of work is calculated by multiplying their combined rate by the time taken: Total Work = 3x * 16 days = 48x units.
To find the time B takes alone, divide the total work by B's individual rate: Time for B = 48x / x = 48 days.

Option A: This is an incorrect calculation and does not logically follow from the problem's parameters.
Option C: This might result from miscalculation, such as incorrectly multiplying the combined efficiency and time (e.g., 3x * 12 instead of 3x * 16).
Option D: This is the time it would take for person A to complete the work alone, not person B.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Work and Time problem involving relative efficiency as background academic context rather than a clinical decision trigger.
This type of logical reasoning is a foundational skill for aptitude tests required for many professional entrance exams.
Understanding ratios and proportions is crucial for tasks like calculating medication dosages, resource allocation, and staff scheduling in a clinical setting.
What if A's efficiency was half that of B? In that case, A's rate would be x/2. Their combined rate would be 1.5x. Total work would be 1.5x * 16 = 24x. B's time alone would be 24x / x = 24 days.

How to Approach the Question

First, carefully read the question to understand the relationship between the workers' efficiencies (A is twice as efficient as B).
Assign a variable, like 'x', to represent the work rate (efficiency) of the less efficient person (B). Then express the other person's efficiency in terms of x (A's efficiency = 2x).
Calculate the combined efficiency by adding their individual efficiencies (x + 2x = 3x).
Use the formula: Total Work = Combined Efficiency × Time Taken. This gives you the total amount of work in terms of 'x'.
Finally, calculate the time required for the individual in question (B) by using the formula: Time = Total Work / Individual Efficiency.
Double-check that you have answered the question asked (time for B) and not for the other person (A), as this is a common distractor.

Concept Tested & Keywords

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