A is thrice as good a workman as B and takes 32 days less than B. In how many days can they do the work by working together?

Appeared in: DSSSB - 29 August 2019 (Shift-2)

Explanation

The core principle is that time is inversely proportional to efficiency. Since A is 3 times as efficient as B, A takes 1/3 of the time B takes.
Let the time taken by A be 'x' days and by B be '3x' days. The difference in time is given as 32 days, leading to the equation 3x - x = 32.
Solving the equation gives x = 16. Thus, A takes 16 days and B takes 48 days.
The combined work rate is the sum of their individual rates: (1/16) + (1/48) = 4/48 = 1/12 of the work per day.
The total time to complete the work together is the reciprocal of the combined work rate, which is 12 days.

Option A: This is an incorrect value, likely resulting from a calculation error when determining the individual times or when adding the fractions for the combined work rate.
Option B: This value is also a result of a calculation mistake. It does not align with the correct formula for combining work rates.
Option C: This is an incorrect answer. A common mistake could be incorrectly simplifying the fraction 4/48 or miscalculating the sum of 1/16 and 1/48.

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 focusing on problems involving the inverse relationship between efficiency and time as background academic context rather than a clinical decision trigger.
While not a clinical question, quantitative aptitude is a crucial skill for nurses.
Nurses regularly perform calculations for medication dosages, IV drip rates, and fluid balance, where accuracy is critical for patient safety.
What if? If A were only twice as good as B, the time difference would lead to A taking 32 days and B taking 64 days. Their combined time would be approximately 21.33 days (1/32 + 1/64 = 3/64).

How to Approach the Question

First, identify the relationship between the workers' efficiencies. Here, A is 3 times as efficient as B (Ratio 3:1).
Recognize that time taken is inversely proportional to efficiency. Therefore, the ratio of time taken by A to B is 1:3.
Translate this relationship into an algebraic equation. Let time for A = x, so time for B = 3x.
Use the given information about the time difference to solve for 'x'. The problem states A takes 32 days less than B, so 3x - x = 32.
After finding the individual times (A=16 days, B=48 days), calculate their combined daily work rate by adding the reciprocals of their individual times (1/16 + 1/48).
The final answer is the reciprocal of the combined daily work rate.

Concept Tested & Keywords

Concept Tested: This question tests the concept of 'Work and Time' from quantitative aptitude, specifically focusing on problems involving the inverse relationship between efficiency and time.
Stem keywords: thrice as good, workman, days less, working together
Lead-in keywords: how many days

Q4UIsJhLaudGCV4WQnixN-

Practise the full DSSSB - 29 August 2019 (Shift-2)

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