Hamesh can do a piece of work in 6 days and Suresh can do it in 12 days. How many days will be required for both to do the same work together?

1. A

   2

2. B

   3

3. C

   4

4. D

   5

Appeared in: RML 2023

Explanation

• The core principle is to determine the fraction of work each person completes per day (their work rate).
• Hamesh's daily work rate is 1/6, and Suresh's is 1/12.
• Their combined daily work rate is the sum of their individual rates: (1/6) + (1/12) = 3/12 = 1/4.
• If they complete 1/4 of the work together in one day, the total time to complete the entire work is the reciprocal of this rate, which is 4 days.

Why Other Options Were Wrong

• Option A: This is an incorrect calculation. A time of 2 days would require a combined work rate of 1/2 per day, but the actual combined rate is 1/4 per day.
• Option B: This is an incorrect calculation. A time of 3 days would require a combined work rate of 1/3 per day. The sum of 1/6 and 1/12 is 1/4.
• Option D: This answer is logically impossible. Since Hamesh can complete the work alone in 6 days, the combined effort must result in a time less than 6 days.

Related Visual

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 by calculating combined work rates as background academic context rather than a clinical decision trigger.
• While not a direct clinical skill, quantitative aptitude is a component of many nursing entrance and recruitment exams.
• These questions assess analytical and problem-solving abilities, which are crucial for nurses in clinical decision-making.
• Skills used here are transferable to calculating medication dosages, IV drip rates, and managing time-sensitive patient care schedules.

How to Approach the Question

• First, identify the question type as a 'Time and Work' problem.
• Determine the time each individual takes to complete the work alone (Person A = T1, Person B = T2). Here, T1=6 and T2=12.
• Calculate the work rate for each person. The rate is the reciprocal of the time (Rate A = 1/T1, Rate B = 1/T2). Here, rates are 1/6 and 1/12.
• Add the individual rates to find the combined work rate: (1/T1 + 1/T2).
• The total time taken to complete the work together is the reciprocal of the combined rate: 1 / (Combined Rate).
• Finally, verify that the answer is logical—it must be less than the shortest individual time.

Concept Tested & Keywords

• Concept Tested: Solving 'Time and Work' problems by calculating combined work rates.
• Stem keywords: piece of work, 6 days, 12 days, work together
• Lead-in keywords: How many days

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