Amarjeet works 5 times as fast as Dileep. If Dileep can complete a work in 25 days, the time they can finish the work together is:

Appeared in: RRB Nsg. Superintendent -29 April-2025 (shift-2nd)

Explanation

Dileep's daily work rate is 1/25 of the job, as he takes 25 days to complete it.
Amarjeet works 5 times faster, so his daily work rate is 5 × (1/25) = 5/25 or 1/5 of the job.
When working together, their rates are added: (1/25) + (5/25) = 6/25 of the job per day.
The total time to complete the job is the reciprocal of the combined rate: 1 / (6/25) = 25/6 days.
Converting the improper fraction 25/6 to a mixed number results in 4 with a remainder of 1, which is written as 4 1/6 days.

Option A: This option, 4 3/6 days, simplifies to 4 1/2 or 4.5 days. This value is incorrect and would arise from a miscalculation of the combined work rate.
Option B: This option, 3 1/6 days, is equivalent to 19/6 days. This is significantly less than the correctly calculated time of 25/6 days.
Option D: This option, 4 5/6 days, is equivalent to 29/6 days. This is more than the correctly calculated time and likely stems from an error in adding the fractions.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Work and Time as background academic context rather than a clinical decision trigger.
This question assesses quantitative aptitude, a component of the non-nursing section in many nursing competitive examinations.
While not a direct clinical scenario, the logical reasoning and mathematical precision required are foundational skills for nurses, especially in areas like medication dosage calculation and fluid balance monitoring.
What if Amarjeet was only twice as fast? His rate would be 2/25. The combined rate would be (1/25) + (2/25) = 3/25. The time taken would be 25/3 days, or 8 1/3 days.

How to Approach the Question

First, identify the individual time taken by one person (Dileep takes 25 days).
Convert this time into a daily work rate. The rate is the reciprocal of the time (Dileep's rate = 1/25).
Calculate the other person's work rate based on the given relationship (Amarjeet is 5 times faster, so his rate is 5 × 1/25).
Add the individual rates to find their combined daily work rate.
The total time to complete the work together is the reciprocal of this combined rate.
Finally, convert the resulting fraction into the format required by the options (a mixed number).

Concept Tested & Keywords

Concept Tested: Work and Time
Stem keywords: works 5 times as fast, complete a work, 25 days, finish the work together
Lead-in keywords: the time

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Practise the full RRB Nsg. Superintendent -29 April-2025 (shift-2nd)

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