A can do a piece of work in 12 days and B can do it in 18 days. They work together for 2 days and then A leaves. How long will B take to finish the remaining work?

Appeared in: NORCET 3 - 2022 (Shift-1)

Explanation

A's 1-day work is 1/12 and B's 1-day work is 1/18.
Their combined work for one day is the sum of their individual rates: (1/12) + (1/18) = 5/36 of the work.
In the 2 days they work together, they complete 2 * (5/36) = 10/36 = 5/18 of the total work.
The work remaining after A leaves is 1 - 5/18 = 13/18.
To find the time B takes to finish this remaining work, we divide the remaining work by B's daily work rate: (13/18) / (1/18).
This calculation simplifies to (13/18) * 18 = 13 days.

Option A: This is an incorrect calculation. It might result from errors in calculating the remaining work or dividing it by B's work rate.
Option B: This is an incorrect calculation. It does not follow from the correct application of the work and time formulas.
Option C: This is an incorrect calculation. A common mistake could be to subtract the number of days worked (2) from the total days B would take (18-2=16) or some other flawed logic.

Visual 1: Flowchart: A step-by-step visual guide to solving work-and-time problems. It would show the process from finding individual rates, calculating combined work, determining remaining work, and finally calculating the time to finish.

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, specifically dealing with combined work, partial work completion, and remaining work as background academic context rather than a clinical decision trigger.
This is a quantitative aptitude question designed to test logical reasoning and mathematical problem-solving skills.
While not a direct clinical scenario, the ability to perform multi-step calculations is a foundational skill for nurses.
This skill is essential for critical tasks such as calculating medication dosages, determining IV drip rates, and monitoring fluid intake and output, all of which require precision.

How to Approach the Question

First, identify the individual rates of work. The rate is the reciprocal of the time taken (e.g., if time is 12 days, the rate is 1/12 of the work per day).
Calculate the combined rate of work by adding the individual rates.
Multiply the combined rate by the number of days they worked together to find the fraction of work completed.
Subtract the completed work from 1 (representing the total work) to find the fraction of remaining work.
Divide the remaining work by the rate of the person who will finish the job to find the number of days required.
Carefully check your arithmetic, especially with fractions and LCM calculations, to select the correct option.

Concept Tested & Keywords

Concept Tested: This question tests the concept of 'Work and Time' from quantitative aptitude, specifically dealing with combined work, partial work completion, and remaining work.
Stem keywords: A can do a piece of work, 12 days, B can do it, 18 days, work together for 2 days, A leaves, B take to finish the remaining work
Lead-in keywords: How long will

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Practise the full NORCET 3 - 2022 (Shift-1)

Attempt every question from this paper in a timed mock, then review the full solution for each one.