A and B can do a job in 25 days and 29 days, respectively. A works alone for 13 days and leaves. The number of days required by B to complete the remaining job is:

1. A

   13 23/29

2. B

   13 23/25

3. C

   13 29/23

4. D

   13 23/25

Appeared in: DSSSB 6 September 2024

Explanation

• First, calculate the fraction of work A completes. A's daily work rate is 1/25, so in 13 days, A finishes 13 × (1/25) = 13/25 of the job.
• Next, find the remaining work. The total job is 1 unit, so the remaining portion is 1 - 13/25 = 12/25.
• B's daily work rate is 1/29 of the job per day.
• To find the number of days B needs to complete the rest of the job, divide the remaining work by B's daily rate.
• The calculation is (12/25) ÷ (1/29), which is equivalent to (12/25) × 29 = 348/25.
• Converting the improper fraction 348/25 to a mixed number gives 13 with a remainder of 23, resulting in 13 23/25 days.

Why Other Options Were Wrong

• Option A: This result is obtained if the final calculation is (12/29) × 29, which is incorrect. The denominator of the remaining work fraction should be 25 (from A's total time), not 29.
• Option C: This option incorrectly inverts the final fraction (29/23 instead of 23/25). In a mixed number, the numerator of the fraction part cannot be larger than the denominator.
• Option D: This option is identical to the correct option B. In a standardized test, having two identical correct options is an error in question design. While the value is correct, only one option can be selected as the answer.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation of time and work, specifically determining the time required to complete remaining work as background academic context rather than a clinical decision trigger.
• Understanding work-rate problems is fundamental for resource planning and management, a skill applicable in various fields, including managing staff assignments and project timelines in a healthcare setting.
• This type of calculation helps in estimating task completion times when resources (personnel) change, ensuring efficient workflow and preventing delays in patient care or administrative processes.
• What if? If B had worked for 13 days instead of A, the remaining work would be 1 - 13/29 = 16/29. A would then take (16/29) ÷ (1/25) = 400/29 = 13 23/29 days to finish.

How to Approach the Question

• First, identify the individual work rates for each person. The rate is the reciprocal of the time taken (e.g., rate = 1/time). A's rate is 1/25 per day, and B's is 1/29 per day.
• Calculate the amount of work completed by the person who works first. Here, A works for 13 days, so the work done is 13 × (1/25) = 13/25.
• Determine the remaining portion of the work. The total work is always considered 1 unit. So, remaining work = 1 - (work done) = 1 - 13/25 = 12/25.
• Calculate the time the second person will take to finish this remaining work using the formula: Time = Remaining Work / Second Person's Work Rate.
• Substitute the values: Time = (12/25) ÷ (1/29).
• Solve the division of fractions by multiplying by the reciprocal: (12/25) × 29 = 348/25. Convert this improper fraction to a mixed number to match the format of the options.

Concept Tested & Keywords

• Concept Tested: Calculation of time and work, specifically determining the time required to complete remaining work.
• Stem keywords: A and B, do a job, 25 days, 29 days, A works alone, 13 days
• Lead-in keywords: number of days required

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QmA6mpi1sWJ5NpyONfxPBB

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