A can do a work in 16 days and B can do the work in 24 days. If they work together for 4 days, what fraction of work is left?

Appeared in: DSSSB - 28 August 2019 (Shift-1)

Explanation

The core of this problem is to determine the fraction of work left after a period of collaborative effort.
A's one-day work is 1/16 and B's is 1/24. Their combined one-day work is the sum: 1/16 + 1/24 = (3 + 2)/48 = 5/48.
In 4 days, they complete 4 * (5/48) = 20/48 = 5/12 of the work.
The total work is represented by 1. The remaining work is calculated by subtracting the completed work from the total: 1 - 5/12 = 7/12.

Option A: This fraction (5/6) is equivalent to 10/12. It is an incorrect calculation and does not correspond to either the work done or the work left.
Option C: This fraction represents the amount of work that has been completed by A and B in 4 days, not the amount of work that is left.
Option D: This fraction (3/4) is equivalent to 9/12. It is an incorrect calculation and does not relate to the work done or remaining.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating remaining work in a Time and Work problem as background academic context rather than a clinical decision trigger.
While not a direct clinical skill, quantitative aptitude is a key component of entrance and recruitment exams for nursing programs and positions.
Proficiency in these types of problems demonstrates logical reasoning and numerical skills, which are foundational for clinical calculations like medication dosage, IV drip rates, and fluid balance monitoring.
What if? If the question asked for the fraction of work completed, the answer would be 5/12. This highlights the importance of carefully reading the question to determine exactly what is being asked.

How to Approach the Question

First, determine the rate of work for each individual per day. A's rate is 1/16 and B's rate is 1/24.
Calculate their combined rate of work by adding their individual rates: 1/16 + 1/24.
Find the total amount of work they complete together by multiplying their combined daily rate by the number of days they worked (4 days).
Carefully read the question's prompt. Note that it asks for the fraction of work 'left', not 'done'.
Subtract the fraction of work completed from 1 (representing the whole task) to find the fraction of work remaining.

Concept Tested & Keywords

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Practise the full DSSSB - 28 August 2019 (Shift-1)

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