A can do a piece of work in 16 hours, B and C can do it in 8 hours while A and C can do it in 12 hours. How long will B alone take to do it?

Appeared in: DSSSB -28 August 2019 (Shift-2)

Explanation

The core concept is to convert time into work rate (Rate = 1/Time).
First, calculate C's individual work rate by subtracting A's rate (1/16) from the combined rate of A and C (1/12). This gives C's rate as 1/48.
Next, calculate B's individual work rate by subtracting C's rate (1/48) from the combined rate of B and C (1/8). This gives B's rate as 5/48.
Finally, convert B's work rate back into time (Time = 1/Rate). Time for B = 1 / (5/48) = 48/5 = 9.6 hours.

Option A: This value is a result of incorrect arithmetic operations when combining the fractions for the work rates.
Option B: This value is a result of miscalculation. For instance, it might arise from incorrectly finding the common denominator or subtracting the fractions.
Option C: This value is an incorrect result, likely stemming from an error in the subtraction or inversion steps of the calculation.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Work and Time Problems as background academic context rather than a clinical decision trigger.
This is a general aptitude question, not a clinical one. It tests logical reasoning and mathematical problem-solving skills, which are essential for nurses in tasks like calculating medication dosages, infusion rates, and managing time-sensitive patient care schedules.
Strong analytical skills help in interpreting patient data, prioritizing tasks, and making sound clinical judgments under pressure.
What if the question asked for the time taken if A, B, and C worked together? You would sum their individual rates (A=1/16, B=5/48, C=1/48). Total rate = (3+5+1)/48 = 9/48 = 3/16. Total time = 16/3 ≈ 5.33 hours.

How to Approach the Question

First, identify the question type. This is a quantitative aptitude problem involving 'Work and Time'.
The key is to convert the time taken to complete a task into a 'work rate'. The formula is Rate = 1 / Time.
List the work rates for each individual or group based on the given information: A's rate = 1/16, (B+C)'s rate = 1/8, (A+C)'s rate = 1/12.
Formulate a plan to isolate the unknown variable. To find B's rate, you first need to find C's rate.
Execute the plan by setting up and solving the equations: C's rate = (A+C)'s rate - A's rate. Then, B's rate = (B+C)'s rate - C's rate.
Once you find the required work rate (B's rate), convert it back to time using the formula: Time = 1 / Rate. Double-check your arithmetic, especially with fractions.

Concept Tested & Keywords

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Practise the full DSSSB -28 August 2019 (Shift-2)

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