A and B can do a job in 24 days and 13 days, respectively. A works alone for 19 days and leaves. The number of days required by B to complete the remaining job is:

1. A

   2 20/24

2. B

   2 17/24

3. C

   2 15/24

4. D

   2 14/24

Appeared in: DSSSB 14 August 2024

Explanation

• First, determine the fraction of work remaining after A works for 19 days. A's work rate is 1/24 per day, so in 19 days, A completes 19/24 of the job.
• The remaining work is calculated as 1 (total work) minus the work done by A: 1 - 19/24 = 5/24.
• Next, calculate the time B needs to complete this remaining 5/24 of the work. B's work rate is 1/13 per day.
• The time required for B is the remaining work divided by B's work rate: (5/24) ÷ (1/13).
• This calculation is equivalent to multiplying by the reciprocal: (5/24) × 13 = 65/24 days.
• Finally, convert the improper fraction 65/24 to a mixed number. 65 divided by 24 is 2 with a remainder of 17, which gives 2 17/24 days.

Why Other Options Were Wrong

• Option A: This is incorrect. This value might result from a calculation error, such as miscalculating the remaining work or inverting the wrong fraction during division.
• Option C: This is incorrect. This value could be obtained by miscalculating the remainder when dividing 65 by 24 (e.g., 65 - 50 instead of 65 - 48).
• Option D: This is incorrect. This is another possible result of a simple arithmetic mistake during the division or fraction conversion steps.

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Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving 'Time and Work' problems in quantitative aptitude as background academic context rather than a clinical decision trigger.
• This question tests quantitative aptitude, a key component of the non-nursing section of many nursing entrance exams.
• Proficiency in 'Time and Work' problems demonstrates logical reasoning and mathematical skills necessary for various analytical tasks.
• What if A and B worked together for the first 5 days? The approach would change: first, calculate their combined daily work (1/24 + 1/13), then find the work done in 5 days, calculate the remaining work, and finally find the time for the next person to complete it.

How to Approach the Question

• First, identify the individual rates of work. If a person takes 'x' days to do a job, their one-day work is 1/x.
• In this problem, A's 1-day work is 1/24 and B's is 1/13.
• Calculate the amount of work completed by the first person. Here, A works for 19 days, so the work done is 19 × (1/24) = 19/24.
• Determine the remaining portion of the work by subtracting the completed work from the total work (which is always assumed to be 1). Remaining work = 1 - 19/24 = 5/24.
• Finally, calculate the time the next person needs to finish this remaining work. This is found by dividing the remaining work by their one-day work rate. Time for B = (Remaining Work) ÷ (B's 1-day work).
• Simplify the final expression: (5/24) ÷ (1/13) = (5/24) × 13 = 65/24. Convert to a mixed number if the options are in that format.

Concept Tested & Keywords

• Concept Tested: Solving 'Time and Work' problems in quantitative aptitude.
• Stem keywords: A and B, do a job, 24 days, 13 days, A works alone, 19 days
• Lead-in keywords: number of days required

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