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

1. A

   2

2. B

   3

3. C

   4

4. D

   5

Appeared in: RML Lucknow - 2021

Explanation

• The core concept is to determine the combined rate of work and then calculate the total time required.
• Ramesh's daily work rate is 1/6 of the total work.
• Suresh's daily work rate is 1/12 of the total work.
• Their combined daily work rate is (1/6) + (1/12) = (2+1)/12 = 3/12 = 1/4 of the work.
• If they complete 1/4 of the work each day, the total time to complete the work is the reciprocal, which is 4 days.

Why Other Options Were Wrong

• Option A: This is incorrect. 2 days would imply a combined work rate of 1/2 per day, which is much faster than their actual combined rate of 1/4.
• Option B: This is incorrect. 3 days would imply a combined work rate of 1/3 per day. This might be chosen by mistakenly averaging the days (6+12)/2 = 9 and then dividing incorrectly.
• Option D: This is an arbitrary incorrect value. It does not correspond to any logical calculation based on the given rates.

Related Visual

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 quantitative aptitude as background academic context rather than a clinical decision trigger.
• This question assesses quantitative aptitude, a skill required for various competitive examinations, including those for nursing positions, to evaluate problem-solving and logical reasoning abilities.
• While not a direct clinical skill, the logical thinking process used here is analogous to resource and time management in a clinical setting, such as planning patient care tasks over a shift.
• What if Suresh was twice as fast (i.e., took 3 days)? The combined rate would be (1/6) + (1/3) = 1/2, and the work would be completed in 2 days.

How to Approach the Question

• First, identify the individual rates of work for each person. The rate is the reciprocal of the time taken (e.g., if time is 6 days, rate is 1/6 per day).
• Second, add the individual rates to find the combined rate of work when they work together.
• Third, calculate the total time required by taking the reciprocal of the combined work rate.
• Alternatively, use the LCM method: assume total work is the LCM of the given days, calculate individual efficiency (units per day), sum the efficiencies, and divide the total work by the combined efficiency.
• Cross-verify your answer. The time taken together must be less than the shortest individual time (4 days is less than 6 days).

Concept Tested & Keywords

• Concept Tested: This question tests the concept of 'Work and Time' from quantitative aptitude.
• Stem keywords: work, days, together
• Lead-in keywords: How many days

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