A and B can do a job in 9 days and 20 days, respectively. A works alone for 5 days and leaves. The number of days required by B to complete the remaining job is:

1. A

   8 8/9

2. B

   8 9/9

3. C

   8 0/9

4. D

   8 5/9

Appeared in: DSSSB 13 August 2024

Explanation

• First, calculate the fraction of work A completes in 5 days: A's rate is 1/9 per day, so in 5 days, A completes 5 * (1/9) = 5/9 of the job.
• Next, find the remaining work: Total work is 1, so the remaining portion is 1 - 5/9 = 4/9.
• Finally, calculate the time B needs to finish this remaining work. B's rate is 1/20 per day.
• Time = Work / Rate = (4/9) / (1/20) = (4/9) * 20 = 80/9 days.
• Converting the improper fraction 80/9 to a mixed number gives 8 8/9 days.

Why Other Options Were Wrong

• Option B: This option, 8 9/9, simplifies to 9. This would mean B takes exactly 9 days. The correct calculation results in 80/9, not 81/9.
• Option C: This option, 8 0/9, simplifies to 8. This would mean B completes the remaining work in exactly 8 days. In 8 days, B would complete 8 * (1/20) = 8/20 = 2/5 of the job. However, the remaining work is 4/9, which is not equal to 2/5.
• Option D: This option, 8 5/9, is equal to 77/9. This does not match the calculated time of 80/9 days required for B to finish the remaining 4/9 of the work.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Time and Work as background academic context rather than a clinical decision trigger.
• While this is a mathematics question, the underlying principle of calculating rates and workload is crucial in healthcare management.
• It applies to staff scheduling, ensuring adequate nurse-to-patient ratios over a shift.
• It is also relevant for resource management, such as calculating the consumption rate of medical supplies to predict when to reorder.

How to Approach the Question

• Identify the time each person takes to complete the job individually. From this, calculate their daily work rate (which is the reciprocal of the time taken).
• Calculate the amount of work done by the first person (A) during the time they worked alone.
• Subtract the work done by A from the total work (assumed as 1 unit) to find the remaining work.
• Divide the remaining work by the daily work rate of the second person (B) to find the number of days B will take to finish.
• Convert the final fraction into a mixed number if necessary to match the options.

Concept Tested & Keywords

• Concept Tested: Time and Work
• Stem keywords: A and B, job, 9 days, 20 days, works alone for 5 days
• Lead-in keywords: number of days required
• Negative lead-in flag: false

Question ID

QbVLLPxWzsmpg5vFAuqgdD

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