If A can do a work in 84 days and B is twice as efficient as A. In how many more days will the work be completed if B joins A on the 22nd day?

Appeared in: DSSSB - 29 August 2019 (Shift-1)

Explanation

A's rate is 1/84 of the work per day. Since B is twice as efficient, B's rate is 2 × (1/84) = 1/42 of the work per day.
A works alone for 21 days (as B joins on the 22nd day), completing 21 × (1/84) = 1/4 of the total work.
The remaining portion of the work is 1 - 1/4 = 3/4.
When working together, their combined rate is (1/84) + (1/42) = 3/84 = 1/28 of the work per day.
The time required to finish the remaining 3/4 of the work is calculated by dividing the remaining work by the combined rate: (3/4) ÷ (1/28) = (3/4) × 28 = 21 days.

Option A: This value (10.5) is exactly half of the correct answer. This error could occur if one miscalculates the remaining work as half of what it should be or incorrectly divides the final answer by two.
Option B: This is a close but incorrect estimate. Such an error might arise from rounding during intermediate steps or a slight miscalculation of the combined work rate.
Option C: This value could result from an error in calculating the initial work done by A. For instance, if one assumed A worked for a different number of days before B joined.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Time and Work problems involving relative efficiency and sequential work as background academic context rather than a clinical decision trigger.
This is a non-clinical, general aptitude question designed to test logical reasoning and mathematical skills.
While not a direct clinical task, proficiency in quantitative aptitude is valuable for nurses. It underpins critical skills such as accurate drug dosage calculation, managing infusion rates, and interpreting patient data charts.
What if B was only 50% more efficient than A? Then B's rate would be 1.5 × (1/84) = 1/56. The combined rate would be (1/84) + (1/56) = (2+3)/168 = 5/168. The time to finish the remaining 3/4 work would be (3/4) ÷ (5/168) = (3/4) × (168/5) = 126/5 = 25.2 days.

How to Approach the Question

First, break down the problem into individual components: A's work rate, B's work rate, the period A works alone, and the period they work together.
Represent the total work as '1' unit. Calculate the fraction of work each person completes in one day (their 'rate'). A's rate is 1/84.
Use the efficiency information to find B's rate. 'Twice as efficient' means B's rate is 2 × A's rate, which is 2 × (1/84) = 1/42.
Calculate the work done during the initial phase. A works alone for 21 days (since B joins on the 22nd), so work done is 21 × (1/84) = 1/4.
Determine the remaining work by subtracting the completed work from the total: 1 - 1/4 = 3/4.
Calculate the combined work rate for the final phase by adding the individual rates: (1/84) + (1/42) = 1/28.

Concept Tested & Keywords

Concept Tested: Time and Work problems involving relative efficiency and sequential work.
Stem keywords: work, days, efficient, joins
Lead-in keywords: how many more days

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Practise the full DSSSB - 29 August 2019 (Shift-1)

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