A can do a job in 24 days, B can do it in 16 days. With the help of C, they do it in 6 days. In how many days can C do the job alone?

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

Explanation

The core concept is that the combined work rate is the sum of individual work rates.
A's daily work is 1/24, and B's is 1/16. Their combined daily work is (1/24 + 1/16) = 5/48.
The combined daily work of A, B, and C is 1/6.
To find C's daily work, subtract A and B's combined work from the total: 1/6 - 5/48.
This simplifies to (8/48 - 5/48) = 3/48 = 1/16.
If C completes 1/16 of the job per day, the total time taken is the reciprocal, which is 16 days.

Option B: This value (48) is the Least Common Multiple (LCM) of the time values (24, 16, 6). It is often used as a hypothetical total unit of work for easier calculation but does not represent the time taken by C.
Option C: This is an incorrect calculation. It does not result from any logical step in solving the work-rate problem.
Option D: This is an incorrect calculation. It does not result from any logical step in solving the work-rate problem.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Work and Time as background academic context rather than a clinical decision trigger.
This question tests logical reasoning and mathematical aptitude, which are essential skills for problem-solving in any professional field.
Accuracy in calculation is crucial for tasks such as medication dosage, fluid balance monitoring, and interpreting lab results.
The ability to break down a complex problem into smaller, manageable parts is a key competency for nurses when managing patient care plans.

How to Approach the Question

Identify the question type: This is a 'Work and Time' problem.
List the knowns: Time for A = 24 days, Time for B = 16 days, Time for A+B+C = 6 days.
Determine the goal: Find the time for C to do the job alone.
Convert times to rates (work per day): Rate = 1/Time. So, A's rate = 1/24, B's rate = 1/16, (A+B+C)'s rate = 1/6.
Set up the equation: C's Rate = (A+B+C)'s Rate - (A's Rate + B's Rate).
Calculate C's rate: 1/6 - (1/24 + 1/16). Solve this to get 1/16.

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.