Akash can complete a piece of work alone in 8 days and Prakash can complete the same piece of work alone in 14 days. They started the work together, but Akash had to leave 4 days before the completion of the work. In how many days will the work complete?

1. A

   7 10/11 days

2. B

   7 12/11 days

3. C

   7 7/11 days

4. D

   7 8/11 days

Appeared in: DSSSB 14 August 2024

Explanation

• derived using the LCM method to define total work units and individual efficiency.
• First, calculate the work done by Prakash alone for the last 4 days (4 days × 4 units/day = 16 units).
• Subtract this from the total work (56 units) to find the work done together: 56 - 16 = 40 units.
• Calculate the time they worked together by dividing the remaining work by their combined efficiency: 40 units / (7+4 units/day) = 40/11 days.
• The total time is the sum of the time they worked together and the time Prakash worked alone: 40/11 + 4 days = 84/11 days.
• Converting 84/11 to a mixed fraction gives 7 7/11 days.

Why Other Options Were Wrong

• Option A: This result (87/11 days) would stem from a calculation error, possibly in determining the remaining work or the total time.
• Option B: This option is an improper mixed fraction (12/11 is greater than 1). The correct calculation leads to 84/11, not 89/11.
• Option D: This result (85/11 days) is a close but incorrect answer, likely due to a minor arithmetic mistake during the calculation of total time or remaining work.

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Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Quantitative Aptitude: Work and Time as background academic context rather than a clinical decision trigger.
• This question tests general quantitative aptitude, a component of many nursing entrance and recruitment examinations.
• Strong analytical and problem-solving skills are essential for nurses in tasks like medication dosage calculation, fluid balance monitoring, and interpreting patient data.
• What if Akash left 2 days after starting? The approach would change. You would calculate the work done in the first 2 days together, then find the time Prakash took to finish the remaining work alone.

How to Approach the Question

• First, identify the question type as a 'Work and Time' problem.
• Use the LCM (Least Common Multiple) of the individual days (8 and 14) to establish a total 'unit' of work. Here, LCM is 56 units.
• Calculate the daily work rate (efficiency) for each person: Akash = 56/8 = 7 units/day; Prakash = 56/14 = 4 units/day.
• Analyze the condition: Akash leaves 4 days before completion. This means Prakash works alone for the final 4 days.
• Calculate the work done in the final phase: 4 days × Prakash's rate (4 units/day) = 16 units.
• Determine the work done jointly by subtracting the solo work from the total: 56 - 16 = 40 units.

Concept Tested & Keywords

• Concept Tested: Quantitative Aptitude: Work and Time
• Stem keywords: complete a piece of work, 8 days, 14 days, work together, leave 4 days before completion
• Lead-in keywords: In how many days

Question ID

Q3Idqq6M_iQKFb8OvU94LY

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