A is thrice as good as workman as B and takes 40 days less than B. In how many days can they do the work by working together?

Appeared in: DSSSB - 28 August 2019 (Shift-1)

Explanation

The problem states A is thrice as efficient as B, so their efficiency ratio is 3:1.
Time is inversely proportional to efficiency, so the ratio of time taken by A and B is 1:3.
Let A take 'x' days and B take '3x' days. The difference is 3x - x = 40, which gives x = 20 days for A and 60 days for B.
Their combined daily work is (1/20) + (1/60) = 4/60 = 1/15 of the total work.
Therefore, the total time to complete the work together is the reciprocal of their combined daily work, which is 15 days.

Option B: This is the time taken by worker A to complete the job alone. The question asks for the time taken when they work together.
Option C: This value does not result from any correct calculation based on the problem's data. It might be chosen due to a calculation error, such as misinterpreting the ratios or incorrectly combining the work rates.
Option D: This value is also a result of incorrect calculation. It does not align with the principles of work and time problems.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Work and Time: Inverse Proportionality and Combined Work as background academic context rather than a clinical decision trigger.
This question tests quantitative reasoning and logical problem-solving, which are essential non-clinical skills for nurses.
Nurses use similar logical skills for tasks like medication dosage calculations, managing patient care schedules, and allocating resources efficiently under time pressure.
What if? If A were only twice as good as B, the time ratio would be 1:2. Then 2x - x = 40, so A would take 40 days and B 80 days. Together, they would take 1 / (1/40 + 1/80) = 80/3 or approximately 26.7 days.

How to Approach the Question

First, identify the efficiency ratio from the problem statement (A is thrice as good as B, so A:B = 3:1).
Next, determine the corresponding time ratio. Since time is inversely proportional to efficiency, the time ratio is the inverse of the efficiency ratio (A:B = 1:3).
Set up an algebraic equation using the given time difference. Let A's time be 'x' and B's time be '3x', so 3x - x = 40.
Solve the equation to find the individual times taken by A and B.
Use the formula for combined work: Total Time = 1 / ( (1/Time_A) + (1/Time_B) ).
Calculate the final answer and select the matching option.

Concept Tested & Keywords

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Practise the full DSSSB - 28 August 2019 (Shift-1)

Attempt every question from this paper in a timed mock, then review the full solution for each one.