8 women can complete a work in 10 days and 10 children take 16 days to complete the same work. How many days will 10 women and 12 children take to complete the work?

1. A

   4 days

2. B

   5 days

3. C

   6 days

4. D

   7 days

Appeared in: RRB Staff Nurse Jaipur-6th June 2018

Explanation

• The work rate of one woman is calculated as 1/80 of the total work per day (since 8 women take 10 days, one woman would take 8x10=80 days).
• Similarly, the work rate of one child is 1/160 of the work per day (since 10 children take 16 days, one child would take 10x16=160 days).
• The combined daily work of 10 women and 12 children is the sum of their individual contributions: (10 * 1/80) + (12 * 1/160).
• This simplifies to 1/8 + 3/40. Finding a common denominator gives 5/40 + 3/40 = 8/40, which reduces to 1/5.
• If 1/5 of the work is completed each day, the entire work will be finished in the reciprocal of this rate, which is 5 days.

Why Other Options Were Wrong

• Option A: This answer is incorrect. It might result from an arithmetic error, such as incorrectly simplifying the combined work rate to 1/4.
• Option C: This is an incorrect calculation. It does not correspond to the correct sum of the work rates.
• Option D: This is an incorrect calculation. It does not correspond to the correct sum of the work rates.

Related Visual

• Visual 1: Flowchart: Step-by-step process for solving Time and Work problems. 1. Calculate total 'person-days' for each group. 2. Find the work rate per person per day. 3. Calculate the combined work rate for the new group. 4. Find the total time by taking the reciprocal.

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving 'Time and Work' problems involving different groups of workers as background academic context rather than a clinical decision trigger.
• This question assesses numerical reasoning and problem-solving skills, which are essential components of the general aptitude section of nursing and other competitive exams.
• The ability to break down a complex problem into smaller, manageable steps is a valuable skill in both test-taking and clinical settings for tasks like medication calculation and resource management.
• What if the question asked for the time taken by 4 women and 8 children? The daily work would be (4/80) + (8/160) = 1/20 + 1/20 = 2/20 = 1/10. In this case, it would take them 10 days.

How to Approach the Question

• First, identify the two initial conditions given in the problem: (1) 8 women take 10 days, and (2) 10 children take 16 days.
• The core principle is that the amount of work is constant. Calculate the total work in 'person-days' for each group to find the rate of a single individual.
• Calculate the total 'woman-days': 8 women × 10 days = 80 woman-days. This implies 1 woman can do the work in 80 days, so her daily rate is 1/80.
• Calculate the total 'child-days': 10 children × 16 days = 160 child-days. This implies 1 child can do the work in 160 days, so his daily rate is 1/160.
• Now, calculate the combined daily work rate for the new group (10 women and 12 children) by summing their individual rates: (10 × 1/80) + (12 × 1/160).
• The total time required is the reciprocal of this combined daily work rate. If the rate is '1/x', the time taken is 'x' days.

Concept Tested & Keywords

• Concept Tested: Solving 'Time and Work' problems involving different groups of workers.
• Stem keywords: women, children, complete a work, days
• Lead-in keywords: How many days
• Negative lead-in flag: false

Question ID

QmY6AsphVMDIP8uW4XCG3G

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