A can do a work in 24 days and B can do the work in 32 days. If they work together for 8 days, what fraction of work is left?

Appeared in: DSSSB - 29 August 2019 (Shift-2)

Explanation

The core concept is to calculate work rate as the reciprocal of time (e.g., A's rate is 1/24 of the work per day).
When working together, their individual rates are added. The combined rate is 1/24 + 1/32 = 7/96 of the work per day.
The amount of work completed in 8 days is the combined rate multiplied by the time: (7/96) * 8 = 7/12.
The question asks for the work left, which is the total work (1) minus the work done: 1 - 7/12 = 5/12.

Option A: This fraction (1/3 or 4/12) is an incorrect calculation and does not correspond to either the work done or the work left.
Option B: This is the fraction of the work that was completed by A and B in 8 days, not the fraction of work that is left.
Option D: This fraction (1/2 or 6/12) is an incorrect calculation. It is close to the correct answer of 5/12 but is not precise.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Work and Time problems involving combined work and remaining work as background academic context rather than a clinical decision trigger.
This question tests foundational mathematical skills (fractions, rates) which are essential for various calculations in nursing, such as medication dosage, IV drip rates, and interpreting patient data charts.
Accuracy in fraction calculation is a critical patient safety skill to prevent medication errors.
What if? If they worked for 12 days instead of 8, the work done would be (7/96) * 12 = 7/8. The work left would then be 1 - 7/8 = 1/8.

How to Approach the Question

First, identify the time each person takes to complete the work individually (A = 24 days, B = 32 days).
Calculate the rate of work for each person. The rate is the reciprocal of the time taken (Rate of A = 1/24 per day, Rate of B = 1/32 per day).
Add the individual rates to find their combined rate of work when they work together.
Multiply the combined rate by the number of days they worked (8 days) to find the fraction of work completed.
Finally, subtract the fraction of work completed from 1 (representing the total work) to find the fraction of work that is left.
Carefully read the question to ensure you are answering what is asked (work left vs. work done).

Concept Tested & Keywords

Concept Tested: Work and Time problems involving combined work and remaining work.
Stem keywords: work, 24 days, 32 days, work together, 8 days, fraction of work is left
Lead-in keywords: what fraction

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Practise the full DSSSB - 29 August 2019 (Shift-2)

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