A and B working separately can do a piece of work in 10 and 15 days, respectively. If they work for a day alternately, beginning with A, in how many days will the work be finished?

Appeared in: DSSSB October 2024

Explanation

A's 1-day work is 1/10 and B's 1-day work is 1/15.
They work alternately, so in one 2-day cycle (A then B), the work done is 1/10 + 1/15 = 5/30 = 1/6 of the total work.
To complete the whole work (which is 1, or 6/6), it takes exactly 6 such cycles.
The total time required is 6 cycles multiplied by 2 days per cycle, which equals 12 days.

Option B: This is the time A would take to complete the work alone, not when working alternately with B.
Option C: This is an incorrect calculation. After 10 days (5 cycles), 5/6 of the work is done. On the 11th day, A works and completes another 1/10 of the work. The total work done after 11 days is 5/6 + 1/10 = 28/30, which is less than the full amount.
Option D: This overestimates the time required. The work is finished precisely at the end of the 12th day, so no work is needed on the 13th day.

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 alternate working days as background academic context rather than a clinical decision trigger.
While not a clinical question, quantitative aptitude tests a candidate's logical reasoning and problem-solving skills, which are essential for a nurse in making quick, calculated decisions.
This type of problem-solving is analogous to calculating medication dosages over time or managing patient care schedules efficiently.
What if? If B started the work instead of A, the work done in the first 2-day cycle (B then A) would still be 1/6. The total time to complete the work would remain 12 days because the work is completed exactly at the end of a full cycle.

How to Approach the Question

First, identify the individual rates of work for each person. A's 1-day work is 1/10, and B's 1-day work is 1/15.
Next, determine the work pattern. The problem states they work on alternate days, beginning with A (A, B, A, B...).
Group the work into a single, repeating cycle. For two people working alternately, one cycle consists of 2 days.
Calculate the fraction of work completed in one full cycle by adding the work done by each person (1/10 + 1/15 = 1/6).
Divide the total work (which is always represented as 1) by the fraction of work done per cycle to find the number of cycles needed (1 ÷ 1/6 = 6 cycles).
Finally, multiply the number of cycles by the number of days per cycle to get the total time (6 cycles × 2 days/cycle = 12 days).

Concept Tested & Keywords

Qk_AoY6is3QxaI3uZVqYfQ

Practise the full DSSSB October 2024

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