Alice can do a particular job in 7 days working 9 hours a day, and Bob can do it in 6 days working 7 hours a day. How long will it take them to complete it working together, working 9 hours a day?

1. A

   3 day

2. B

   2 day

3. C

   5 day

4. D

   4 day

Appeared in: ESIC Nursing Officer -2019 (Shift -1)

Explanation

• First, calculate the total hours each person needs to complete the job alone: Alice needs 7 days × 9 hours/day = 63 hours, and Bob needs 6 days × 7 hours/day = 42 hours.
• Next, determine their hourly work rates. Alice's rate is 1/63 of the job per hour, and Bob's rate is 1/42 of the job per hour.
• Combine their hourly rates: (1/63) + (1/42) = (2+3)/126 = 5/126 of the job per hour.
• Calculate the total time in hours to finish the job together, which is the reciprocal of the combined rate: 1 / (5/126) = 126/5 = 25.2 hours.
• Finally, convert the total hours into days based on their 9-hour workday: 25.2 hours / 9 hours/day = 2.8 days.
• Since 2.8 days is not an option, the closest whole number answer is 3 days.

Why Other Options Were Wrong

• Option B: 2 days would mean they complete the job in 2 days × 9 hours/day = 18 hours. This is significantly faster than the calculated 25.2 hours required.
• Option C: 5 days is much longer than the calculated time of 2.8 days. This would imply their combined work rate is much slower.
• Option D: 4 days is also significantly longer than the calculated time of 2.8 days.

Related Visual

• Visual 1: Flowchart: A visual flowchart illustrating the step-by-step calculation: 1. Calculate individual total hours. 2. Find hourly rates. 3. Combine rates. 4. Calculate total combined hours. 5. Convert to days.

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain This question tests the concept of 'Work and Time' from general mathematics and aptitude as background academic context rather than a clinical decision trigger.
• This question assesses quantitative aptitude and logical reasoning, which are essential skills for nurses.
• Nurses often need to perform calculations related to medication dosages, IV drip rates, and patient monitoring, which require a strong foundation in mathematics.
• Problem-solving skills are crucial in the dynamic and often high-pressure healthcare environment.

How to Approach the Question

• First, identify the core task: calculating the combined work time.
• Break down the problem into smaller steps. Start by finding the total time in hours each person takes to do the job alone. This standardizes the unit of work.
• Calculate the 'work rate' for each person. This is the fraction of the job they complete in one hour (e.g., 1/total hours).
• Add the individual work rates to find the combined work rate when they work together.
• The total time to complete the job together is the reciprocal of the combined work rate.
• Finally, ensure your answer matches the units requested in the question. Here, convert the total hours into days by dividing by the number of hours they work per day.

Concept Tested & Keywords

• Concept Tested: This question tests the concept of 'Work and Time' from general mathematics and aptitude.
• Stem keywords: job, days, hours, working together
• Lead-in keywords: How long

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QFG1dxUHsohHAOfWOTH4yH

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