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NORCET 2 - 2021 (shift-1)
Quantitative Aptitude and Mathematics
Medium

A and B together can do a piece of work in 10 days. A alone can do it in 30 days, the time in which B alone can do it is :

Appeared in: NORCET 2 - 2021 (shift-1)

Explanation

  • The fundamental principle is that the work rate of B is the difference between the combined work rate of (A+B) and the work rate of A.
  • The combined work done by A and B in one day is 1/10 of the total work.
  • The work done by A alone in one day is 1/30 of the total work.
  • Therefore, the work done by B alone in one day is (1/10) - (1/30), which equals 2/30 or 1/15.
  • If B completes 1/15 of the work in one day, the total time B will take to complete the work is the reciprocal, which is 15 days.

Why Other Options Were Wrong

  • Option A: This is an incorrect calculation. If B took 20 days, the combined time for A (30 days) and B (20 days) would be 1 / (1/30 + 1/20) = 1 / (5/60) = 12 days, not the 10 days given in the problem.
  • Option C: This is an incorrect calculation. If B took 12 days, the combined time for A (30 days) and B (12 days) would be 1 / (1/30 + 1/12) = 1 / (7/60) ≈ 8.57 days, not 10 days.
  • Option D: This is logically impossible. The time taken by A and B working together is 10 days. B working alone cannot possibly complete the work in the same amount of time as when receiving help from A.

Related Visual

A flowchart illustrating the LCM method: Start with given times 10 and 30 - Find LCM 30 units - Calculate efficiencies A+B\=3, A\=1 - Find Bs efficiency 3-1\=2 - Calculate...
  • Visual 1: Flowchart - A flowchart illustrating the LCM method: Start with given times (10 and 30) -> Find LCM (30 units) -> Calculate efficiencies (A+B=3, A=1) -> Find B's efficiency (3-1=2) -> Calculate B's time (30/2=15).
  • Visual 2: Bar Chart - A chart comparing the work rates (units/day). One bar for A (1 unit/day), one for B (2 units/day), and a combined bar for A+B (3 units/day) to visually represent that A's rate + B's rate = (A+B)'s rate.
Clinical Relevance
  • Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating individual work time from combined work time in 'Time and Work' problems as background academic context rather than a clinical decision trigger.
  • This question tests quantitative aptitude and logical reasoning, which are essential components of many nursing entrance examinations.
  • Strong problem-solving skills are crucial for nurses in clinical practice for tasks like calculating drug dosages, managing IV drip rates, and prioritizing time-sensitive patient care activities.
  • What if? If A alone could do the work in 20 days (instead of 30), B's time would be calculated as 1 / (1/10 - 1/20) = 1 / (1/20) = 20 days. This demonstrates how the efficiency of one person directly impacts the time required by the other.
How to Approach the Question
  • Step 1: Carefully read the question to identify the given information. Time for (A+B) = 10 days. Time for A alone = 30 days.
  • Step 2: Clearly identify what needs to be calculated: The time for B to complete the work alone.
  • Step 3: Choose a suitable method. The 'work per day' (fraction) method or the 'efficiency' (LCM) method are both effective.
  • Step 4: Apply the chosen method. For the fraction method, represent the work rate as 1/time. (A+B)'s rate is 1/10, and A's rate is 1/30.
  • Step 5: Set up the equation to find B's rate: B's rate = (A+B)'s rate - A's rate.
  • Step 6: Solve the equation: 1/10 - 1/30 = 1/15. This is B's work rate.
Concept Tested & Keywords
  • Concept Tested: Calculating individual work time from combined work time in 'Time and Work' problems.
  • Stem keywords: A and B together, piece of work, 10 days, A alone, 30 days, B alone
  • Lead-in keywords: the time in which

Question ID

QRT39iYFQ5dFMLP0FSQrJp

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