A is thrice as good as 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 taken is inversely proportional to efficiency. Since A is 3 times as efficient as B, A takes 1/3 of the time B takes.
Using the given difference in time (32 days), we can set up an algebraic equation (3x - x = 32) to find the individual times taken by A (16 days) and B (48 days).
The combined work rate is the sum of individual work rates (1/16 + 1/48).
The total time taken together is the reciprocal of their combined daily work, which calculates to 12 days (1 / (1/12)).

Option A: This value is incorrect. It may arise from a miscalculation when adding the work rates or an error in solving the initial algebraic equation.
Option B: This is an incorrect result. It could be obtained by making a mistake in the arithmetic, such as incorrectly finding the least common multiple or summing the fractions.
Option C: This value is close but incorrect. It's important to follow the precise mathematical steps rather than estimating. A calculation error is the likely source of this answer.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving problems related to work, time, and efficiency as background academic context rather than a clinical decision trigger.
This question tests quantitative aptitude and logical reasoning, which are essential components of the general intelligence section in many nursing entrance and recruitment examinations.
While not a clinical skill, the ability to perform calculations accurately and quickly is crucial for nurses in tasks like medication dosage calculation, IV drip rate monitoring, and interpreting patient data.
What if A was only twice as good as B? The efficiency ratio would be 2:1, and the time ratio 1:2. The equation would be 2x - x = 32, so x=32. A would take 32 days, B would take 64 days. Together, they would take 1 / (1/32 + 1/64) = 1 / (3/64) = 64/3 ≈ 21.33 days.

How to Approach the Question

First, identify the question type as a 'Work and Time' problem.
Translate the relationship between workers' skills into a numerical efficiency ratio. 'A is thrice as good as B' means the efficiency ratio of A to B is 3:1.
Recall that time is inversely proportional to efficiency. Invert the efficiency ratio to get the time ratio. The time ratio for A to B is 1:3.
Use the given time difference to form an algebraic equation. Let A's time be 'x' and B's time be '3x'. The equation is 3x - x = 32.
Solve the equation to find the individual times for A and B.
Calculate the work done by each person in one day (which is the reciprocal of their total time).

Concept Tested & Keywords

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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.