A, B and C can do a job in 30, 40 and 48 days respectively. In how many days can the work be done if A is assisted by B and C every third day?

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

Explanation

The problem involves a repeating 3-day cycle: A works alone for two days, and then A, B, and C work together on the third day.
First, calculate the work done in one full 3-day cycle. A's rate is 1/30, B's is 1/40, and C's is 1/48. The work in one cycle is (1/30) + (1/30) + (1/30 + 1/40 + 1/48) = 35/240.
After 6 full cycles (18 days), 210/240 of the work is done. The remaining work is 30/240.
On day 19, A does 8/240 work. On day 20, A does another 8/240. This leaves 14/240 of the work.
On day 21, A, B, and C work together at a rate of 19/240. The time to finish the remaining 14/240 of work is (14/240) / (19/240) = 14/19 days.
The total time is 20 full days plus 14/19 of a day, which is approximately 20 + 0.74 = 20.74 days.

Option A: This value is too low. It might result from an error in calculating the work done per cycle or miscalculating the remaining work after the full cycles.
Option C: This value is too high. It might arise from incorrectly calculating the time needed for the final portion of the work, perhaps by rounding up the days.
Option D: This answer incorrectly assumes the work finishes exactly at the end of a full day. The calculation shows that the final part of the work is completed in a fraction of Day 21.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain This question tests the ability to solve problems related to 'Work and Time', specifically involving cyclical work patterns and combined efficiencies as background academic context rather than a clinical decision trigger.
While not a clinical question, this type of logical reasoning and calculation is a core skill tested in the general aptitude section of nursing entrance exams.
Strong analytical and problem-solving skills are essential for nurses in managing time, resources, and patient care schedules effectively.
What if A was assisted by B on the second day and C on the third day? The entire cycle's work calculation would change. The work in 3 days would be (A's work) + (A+B's work) + (A+C's work), leading to a different total time.

How to Approach the Question

First, identify the question type. This is a mathematical problem involving 'Work and Time' with a cyclical pattern.
Break down the problem: list the individual work rates for A, B, and C (1/30, 1/40, 1/48).
Define the repeating cycle: Day 1 (A), Day 2 (A), Day 3 (A+B+C).
Calculate the total work done in one complete cycle. Using the LCM of the denominators (240) simplifies the addition of fractions.
Determine how many full cycles can be completed without finishing the entire job. Multiply the work per cycle by an integer to get close to the total work.
Calculate the remaining work and then calculate, day by day, how long it takes to complete this remaining portion. The final day may be a fraction.

Concept Tested & Keywords

Concept Tested: This question tests the ability to solve problems related to 'Work and Time', specifically involving cyclical work patterns and combined efficiencies.
Stem keywords: A, B and C, do a job, 30, 40 and 48 days, assisted by B and C, every third day
Lead-in keywords: In how many 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.