A and B can finish a piece of work in 23 days and 16 days respectively. A works alone for 20 days and leaves. How many days will B take to finish the remaining work?

1. A

   2 5/23

2. B

   2 1/23

3. C

   2 12/23

4. D

   2 2/23

Appeared in: DSSSB 12 August 2024

Explanation

• First, calculate the fraction of work A completes in 20 days. Since A takes 23 days for the whole job, A's rate is 1/23 per day. In 20 days, A completes 20 × (1/23) = 20/23 of the work.
• Next, find the remaining work. The total work is 1. So, the remaining work is 1 - 20/23 = 3/23.
• Finally, calculate the time B needs to finish this remaining work. B can do the entire job in 16 days.
• Time for B = (Fraction of remaining work) × (Total time B takes for the whole job).
• Time for B = (3/23) × 16 = 48/23 days.
• Converting the improper fraction 48/23 to a mixed number gives 2 2/23 days.

Why Other Options Were Wrong

• Option A: This fraction, 2 5/23, is equivalent to 51/23. This result would stem from an error in calculating the remaining work or in the final multiplication step.
• Option B: This fraction, 2 1/23, is equivalent to 47/23. The correct calculation yields 48/23, so this option is incorrect due to a minor calculation error.
• Option C: This fraction, 2 12/23, is equivalent to 58/23. This is a significant miscalculation and does not align with the problem's data.

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 Problems as background academic context rather than a clinical decision trigger.
• While not a clinical question, the underlying skill of performing accurate, multi-step calculations is critical in nursing.
• Nurses constantly use fractions and ratios for medication dosage calculations. An error similar to miscalculating the work fractions could lead to a dangerous medication error.
• This skill is also essential for calculating IV drip rates, titrating medications, and interpreting fluid balance charts, all of which have direct impacts on patient safety.

How to Approach the Question

• First, identify the individual time each person takes to complete the whole task. Here, A takes 23 days and B takes 16 days.
• Convert these times into daily work rates. A's rate is 1/23 of the work per day.
• Calculate the total amount of work completed by the person who worked first. A worked for 20 days, so the work done is 20 × (1/23) = 20/23.
• Determine the fraction of work that is left to be done. Subtract the completed work from 1 (representing the whole task): 1 - 20/23 = 3/23.
• Calculate the time the second person will take to finish this remaining fraction. Multiply the remaining work by the total time the second person takes for the whole job: (3/23) × 16.
• Simplify the resulting fraction (48/23) into a mixed number (2 2/23) and select the matching option.

Concept Tested & Keywords

• Concept Tested: Time and Work Problems
• Stem keywords: finish a piece of work, works alone, remaining work
• Lead-in keywords: How many days
• Negative lead-in flag: false

Question ID

QEI-P5lnt66N1qjoY_AHxQ

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