A and B can complete a work in 18 days and 15 days respectively. They started the work together, but B left the work a few days before completion. If the work was completed in 12 days, for how many days did A work alone?

1. A

   6

2. B

   8

3. C

   7

4. D

   5

Appeared in: BHU NO - 12 April 2024

Explanation

• The total work was completed in 12 days, and A worked for the entire duration.
• A's contribution over 12 days is 12 * (1/18) = 2/3 of the total work.
• The remaining 1/3 of the work must have been completed by B before leaving.
• The time B worked is calculated by dividing the work B did by B's rate: (1/3) / (1/15) = 5 days.
• This means A and B worked together for 5 days.
• The number of days A worked alone is the total duration minus the days they worked together: 12 - 5 = 7 days.

Why Other Options Were Wrong

• Option A: This is an incorrect calculation with no logical basis in the problem's data.
• Option B: This is an incorrect calculation with no logical basis in the problem's data.
• Option D: This is the number of days B worked on the project before leaving, not the number of days A worked alone.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Work and Time Problems as background academic context rather than a clinical decision trigger.
• This is a non-clinical, general aptitude question.
• The ability to solve such problems is tested in many competitive nursing exams to assess logical and quantitative reasoning skills, which are essential for critical thinking in a clinical setting.
• What if? - If the stem changed one defining clue so that 7 no longer matched, reassess the option whose mechanism, classification, or indication now fits the revised presentation.

How to Approach the Question

• First, determine the rate of work for each individual. The rate is the reciprocal of the time taken to complete the entire work (e.g., A's rate is 1/18 work per day).
• Identify who worked for the entire duration. In this case, A worked for all 12 days.
• Calculate the total amount of work done by the person who worked continuously (A's work = A's rate × 12 days).
• Subtract this amount from the total work (which is 1) to find the remaining work. This remaining portion was done by the person who left (B).
• Calculate the number of days the second person (B) worked by dividing the work they did by their rate.
• This result is the number of days they worked together. To find the days A worked alone, subtract the 'together' days from the total project duration.

Concept Tested & Keywords

• Concept Tested: Work and Time Problems
• Stem keywords: A and B, complete a work, 18 days, 15 days, work together, B left, completed in 12 days
• Lead-in keywords: how many days

Question ID

QfNHa7asFygA5nI3qL_TSQ

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